I. M. Gel’fand and D. B. Fuks :
“Cohomologies of the Lie algebra of vector fields on the circle ,”
Funkcional. Anal. i Priložen.
2 : 4
(1968 ),
pp. 92–93 .
An English translation was published in Funct. Anal. Appl. 2 :4 (1968) .
MR
245035
article
People
BibTeX
@article {key245035m,
AUTHOR = {Gel\cprime fand, I. M. and Fuks, D.
B.},
TITLE = {Cohomologies of the {L}ie algebra of
vector fields on the circle},
JOURNAL = {Funkcional. Anal. i Prilo\v{z}en.},
FJOURNAL = {Funkcional\cprime nyi Analiz i ego Prilo\v{z}enija.
Akademija Nauk SSSR},
VOLUME = {2},
NUMBER = {4},
YEAR = {1968},
PAGES = {92--93},
URL = {http://mi.mathnet.ru/eng/faa2800},
NOTE = {An English translation was published
in \textit{Funct. Anal. Appl.} \textbf{2}:4
(1968). MR:245035.},
ISSN = {0374-1990},
}
I. M. Gel’fand and D. B. Fuks :
“Cohomologies of the Lie algebra of tangent vector fields of a smooth manifold ,”
Funkcional. Anal. i Priložen.
3 : 3
(1969 ),
pp. 32–52 .
An English translation was published in Funct. Anal. Appl. 3 :3 (1969) .
MR
256411
article
People
BibTeX
@article {key256411m,
AUTHOR = {Gel\cprime fand, I. M. and Fuks, D.
B.},
TITLE = {Cohomologies of the {L}ie algebra of
tangent vector fields of a smooth manifold},
JOURNAL = {Funkcional. Anal. i Prilo\v{z}en.},
FJOURNAL = {Funkcional\cprime nyi Analiz i ego Prilo\v{z}enija.
Akademija Nauk SSSR},
VOLUME = {3},
NUMBER = {3},
YEAR = {1969},
PAGES = {32--52},
URL = {http://mi.mathnet.ru/eng/faa2722},
NOTE = {An English translation was published
in \textit{Funct. Anal. Appl.} \textbf{3}:3
(1969). MR:256411.},
ISSN = {0374-1990},
}
I. M. Gel’fand and D. B. Fuks :
“Cohomologies of the Lie algebra of tangent vector fields of a smooth manifold, II ,”
Funkcional. Anal. i Priložen.
4 : 2
(1970 ),
pp. 23–31 .
An English translation was published in Funct. Anal. Appl. 4 :2 (1970) .
MR
285024
article
People
BibTeX
@article {key285024m,
AUTHOR = {Gel\cprime fand, I. M. and Fuks, D.
B.},
TITLE = {Cohomologies of the {L}ie algebra of
tangent vector fields of a smooth manifold,
{II}},
JOURNAL = {Funkcional. Anal. i Prilo\v{z}en.},
FJOURNAL = {Funkcional\cprime nyi Analiz i ego Prilo\v{z}enija.
Akademija Nauk SSSR},
VOLUME = {4},
NUMBER = {2},
YEAR = {1970},
PAGES = {23--31},
URL = {http://mi.mathnet.ru/eng/faa2648},
NOTE = {An English translation was published
in \textit{Funct. Anal. Appl.} \textbf{4}:2
(1970). MR:285024.},
ISSN = {0374-1990},
}
I. M. Gel’fand, D. A. Kazhdan, and D. B. Fuks :
“The actions of infinite-dimensional Lie algebras ,”
Funkcional. Anal. i Priložen.
6 : 1
(1972 ),
pp. 10–15 .
An English translation was published in Funct. Anal. Appl. 6 :1 (1972) .
MR
301767
article
People
BibTeX
@article {key301767m,
AUTHOR = {Gel\cprime fand, I. M. and Kazhdan,
D. A. and Fuks, D. B.},
TITLE = {The actions of infinite-dimensional
{L}ie algebras},
JOURNAL = {Funkcional. Anal. i Prilo\v{z}en.},
FJOURNAL = {Funkcional\cprime nyi Analiz i ego Prilo\v{z}enija.
Akademija Nauk SSSR},
VOLUME = {6},
NUMBER = {1},
YEAR = {1972},
PAGES = {10--15},
URL = {http://mi.mathnet.ru/eng/faa2469},
NOTE = {An English translation was published
in \textit{Funct. Anal. Appl.} \textbf{6}:1
(1972). MR:301767.},
ISSN = {0374-1990},
}
I. M. Gel’fand, D. I. Kalinin, and D. B. Fuks :
“Cohomology of the Lie algebra of Hamiltonian formal vector fields ,”
Funkcional. Anal. i Priložen.
6 : 3
(1972 ),
pp. 25–29 .
An English translation was published in Funct. Anal. Appl. 6 :3 (1973) .
MR
312531
article
People
BibTeX
@article {key312531m,
AUTHOR = {Gel\cprime fand, I. M. and Kalinin,
D. I. and Fuks, D. B.},
TITLE = {Cohomology of the {L}ie algebra of {H}amiltonian
formal vector fields},
JOURNAL = {Funkcional. Anal. i Prilo\v{z}en.},
FJOURNAL = {Funkcional\cprime nyi Analiz i ego Prilo\v{z}enija.
Akademija Nauk SSSR},
VOLUME = {6},
NUMBER = {3},
YEAR = {1972},
PAGES = {25--29},
URL = {http://mi.mathnet.ru/eng/faa2511},
NOTE = {An English translation was published
in \textit{Funct. Anal. Appl.} \textbf{6}:3
(1973). MR:312531.},
ISSN = {0374-1990},
}
D. B. Fuks :
“Characteristic classes of foliations ,”
Usp. Mat. Nauk
28 : 2(170)
(1973 ),
pp. 3–17 .
An English translation was published in Russ. Math. Surv. 28 :2 (1973) .
MR
415635
Zbl
0272.57012
article
BibTeX
@article {key415635m,
AUTHOR = {Fuks, D. B.},
TITLE = {Characteristic classes of foliations},
JOURNAL = {Usp. Mat. Nauk},
FJOURNAL = {Uspekhi Matematicheskikh Nauk [N. S.]},
VOLUME = {28},
NUMBER = {2(170)},
YEAR = {1973},
PAGES = {3--17},
URL = {http://mi.mathnet.ru/eng/umn4859},
NOTE = {An English translation was published
in \textit{Russ. Math. Surv.} \textbf{28}:2
(1973). MR:415635. Zbl:0272.57012.},
ISSN = {0042-1316},
}
D. B. Fuks :
“Quillenization and bordisms ,”
Funkcional. Anal. i Priložen.
8 : 1
(1974 ),
pp. 36–42 .
An English translation was published in Funct. Anal. Appl. 8 :1 (1974) .
MR
343301
article
BibTeX
@article {key343301m,
AUTHOR = {Fuks, D. B.},
TITLE = {Quillenization and bordisms},
JOURNAL = {Funkcional. Anal. i Prilo\v{z}en.},
FJOURNAL = {Funkcional\cprime nyi Analiz i ego Prilo\v{z}enija.
Akademija Nauk SSSR},
VOLUME = {8},
NUMBER = {1},
YEAR = {1974},
PAGES = {36--42},
URL = {http://mi.mathnet.ru/eng/faa2307},
NOTE = {An English translation was published
in \textit{Funct. Anal. Appl.} \textbf{8}:1
(1974). MR:343301.},
ISSN = {0374-1990},
}
I. M. Gel’fand, B. L. Feĭgin, and D. B. Fuks :
“Cohomology of the Lie algebra of formal vector fields with coefficients in its dual space and variations of characteristic classes of foliations ,”
Funkcional. Anal. i Priložen.
8 : 2
(1974 ),
pp. 13–29 .
An English translation was published in Funct. Anal. Appl. 8 :2 (1974) .
MR
356082
article
People
BibTeX
@article {key356082m,
AUTHOR = {Gel\cprime fand, I. M. and Fe\u{\i}gin,
B. L. and Fuks, D. B.},
TITLE = {Cohomology of the {L}ie algebra of formal
vector fields with coefficients in its
dual space and variations of characteristic
classes of foliations},
JOURNAL = {Funkcional. Anal. i Prilo\v{z}en.},
FJOURNAL = {Funkcional\cprime nyi Analiz i ego Prilo\v{z}enija.
Akademija Nauk SSSR},
VOLUME = {8},
NUMBER = {2},
YEAR = {1974},
PAGES = {13--29},
URL = {http://mi.mathnet.ru/eng/faa2326},
NOTE = {An English translation was published
in \textit{Funct. Anal. Appl.} \textbf{8}:2
(1974). MR:356082.},
ISSN = {0374-1990},
}
D. B. Fuks :
“Cohomology of infinite-dimensional Lie algebras and characteristic classes of foliations ,”
pp. 179–285
in
Seriya sovremennye problemy matematiki
[Current problems in mathematics ].
Seriya sovremennye problemy matematiki 10 .
VINITI (Moscow ),
1978 .
An English translation was published in J. Sov. Math. 11 :6 (1978) .
MR
513337
incollection
BibTeX
@incollection {key513337m,
AUTHOR = {Fuks, D. B.},
TITLE = {Cohomology of infinite-dimensional {L}ie
algebras and characteristic classes
of foliations},
BOOKTITLE = {Seriya sovremennye problemy matematiki
[Current problems in mathematics]},
SERIES = {Seriya sovremennye problemy matematiki},
NUMBER = {10},
PUBLISHER = {VINITI},
ADDRESS = {Moscow},
YEAR = {1978},
PAGES = {179--285},
URL = {http://mi.mathnet.ru/eng/intd30},
NOTE = {An English translation was published
in \textit{J. Sov. Math.} \textbf{11}:6
(1978). MR:513337.},
ISSN = {0233-6723},
}
I. M. Gel’fand, B. L. Feigin, and D. B. Fuks :
“Cohomologies of infinite dimensional Lie algebras and Laplace operators ,”
Funkts. Anal. Prilozh.
12 : 4
(1978 ),
pp. 1–5 .
An English translation was published in Funct. Anal. Appl. 12 :4 (1979) .
MR
515625
Zbl
0396.17008
article
People
BibTeX
@article {key515625m,
AUTHOR = {Gel\cprime fand, I. M. and Feigin, B.
L. and Fuks, D. B.},
TITLE = {Cohomologies of infinite dimensional
{L}ie algebras and {L}aplace operators},
JOURNAL = {Funkts. Anal. Prilozh.},
FJOURNAL = {Funktsional'ny\u{\i} Analiz i ego Prilozheniya},
VOLUME = {12},
NUMBER = {4},
YEAR = {1978},
PAGES = {1--5},
URL = {http://mi.mathnet.ru/eng/faa2023},
NOTE = {An English translation was published
in \textit{Funct. Anal. Appl.} \textbf{12}:4
(1979). MR:515625. Zbl:0396.17008.},
ISSN = {0374-1990},
}
B. L. Feĭgin and D. B. Fuks :
“Invariant differential operators on the line ,”
Funkts. Anal. Prilozh.
13 : 4
(1979 ),
pp. 91–92 .
An English translation was published in Funct. Anal. Appl. 13 :4 (1980) .
MR
554429
Zbl
0425.58024
article
People
BibTeX
@article {key554429m,
AUTHOR = {Fe\u{\i}gin, B. L. and Fuks, D. B.},
TITLE = {Invariant differential operators on
the line},
JOURNAL = {Funkts. Anal. Prilozh.},
FJOURNAL = {Funktsional'ny\u{\i} Analiz i ego Prilozheniya},
VOLUME = {13},
NUMBER = {4},
YEAR = {1979},
PAGES = {91--92},
URL = {http://mi.mathnet.ru/eng/faa1955},
NOTE = {An English translation was published
in \textit{Funct. Anal. Appl.} \textbf{13}:4
(1980). MR:554429. Zbl:0425.58024.},
ISSN = {0374-1990},
}
B. L. Feĭgin and D. B. Fuks :
“Invariant skew-symmetric differential operators on the line and Verma modules over the Virasoro algebra ,”
Funct. Anal. Appl.
16 : 2
(1982 ),
pp. 114–126 .
English translation of Russian original published in Funkts. Anal. Prilozh. 16 :2 (1982) .
MR
659165
Zbl
0505.58031
article
Abstract
People
BibTeX
The main result of this article is Theorem 1.1, which gives a complete classification of skew-symmetric differential operators, acting in tensor fields on the line and invariant with respect to diffeomorphisms of the line. The statement of this theorem was stated as a hypothesis in our note [1979].
@article {key0505.58031z,
AUTHOR = {Fe\u{\i}gin, B. L. and Fuks, D. B.},
TITLE = {Invariant skew-symmetric differential
operators on the line and {V}erma modules
over the {V}irasoro algebra},
JOURNAL = {Funct. Anal. Appl.},
FJOURNAL = {Functional Analysis and its Applications},
VOLUME = {16},
NUMBER = {2},
YEAR = {1982},
PAGES = {114--126},
DOI = {10.1007/BF01081626},
NOTE = {English translation of Russian original
published in \textit{Funkts. Anal. Prilozh.}
\textbf{16}:2 (1982). Zbl:0505.58031.},
ISSN = {0016-2663},
}
B. L. Feigin and D. B. Fuks :
“Verma modules over the Virasoro algebra ,”
Funct. Anal. Appl.
17 : 3
(1983 ),
pp. 241–242 .
English translation of Russian original published in Funkts. Anal. Prilozh. 17 :3 (1983) .
Zbl
0529.17010
article
People
BibTeX
@article {key0529.17010z,
AUTHOR = {Feigin, B. L. and Fuks, D. B.},
TITLE = {Verma modules over the {V}irasoro algebra},
JOURNAL = {Funct. Anal. Appl.},
FJOURNAL = {Functional Analysis and its Applications},
VOLUME = {17},
NUMBER = {3},
YEAR = {1983},
PAGES = {241--242},
DOI = {10.1007/BF01078118},
NOTE = {English translation of Russian original
published in \textit{Funkts. Anal. Prilozh.}
\textbf{17}:3 (1983). Zbl:0529.17010.},
ISSN = {0016-2663},
}
D. B. Fuks :
Cohomology of infinite-dimensional Lie algebras .
Contemporary Soviet mathematics .
Consultants Bureau (New York ),
1986 .
English translation of 1984 Russian original .
MR
874337
Zbl
0667.17005
book
BibTeX
@book {key874337m,
AUTHOR = {Fuks, D. B.},
TITLE = {Cohomology of infinite-dimensional {L}ie
algebras},
SERIES = {Contemporary {S}oviet mathematics},
PUBLISHER = {Consultants Bureau},
ADDRESS = {New York},
YEAR = {1986},
PAGES = {xii + 339},
DOI = {10.1007/978-1-4684-8765-7},
NOTE = {English translation of 1984 Russian
original. MR:874337. Zbl:0667.17005.},
ISBN = {9780306109904},
}
B. L. Feigin and D. B. Fuchs :
“Representations of the Virasoro algebra ,”
pp. 465–554
in
Representation of Lie groups and related topics .
Edited by A. M. Vershik and D. P. Zhelobenko .
Advanced Studies in Contemporary Mathematics 7 .
Gordon and Breach (New York ),
1990 .
An earlier version of this appeared as a Stockholm University research report (1986) .
MR
1104280
Zbl
0722.17020
incollection
Abstract
People
BibTeX
@incollection {key1104280m,
AUTHOR = {Feigin, B. L. and Fuchs, D. B.},
TITLE = {Representations of the {V}irasoro algebra},
BOOKTITLE = {Representation of {L}ie groups and related
topics},
EDITOR = {Vershik, A. M. and Zhelobenko, D. P.},
SERIES = {Advanced Studies in Contemporary Mathematics},
NUMBER = {7},
PUBLISHER = {Gordon and Breach},
ADDRESS = {New York},
YEAR = {1990},
PAGES = {465--554},
NOTE = {An earlier version of this appeared
as a Stockholm University research report
(1986). MR:1104280. Zbl:0722.17020.},
ISSN = {0884-0016},
ISBN = {9782881246784},
}