Celebratio Mathematica — Benkart

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Works connected to Vyjayanthi Chari

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Y. Bahturin and G. Benkart: “Highest weight modules for locally finite Lie algebras,” pp. 1–31 in Modular interfaces (18–20 Feburary 1995, Riverside, CA). Edited by V. Chari and I. B. Penkov. AMS/IP Studies in Advanced Mathematics 4. American Mathematical Society (Providence, RI), 1997. MR 1483900 Zbl 0920.17011 incollection

Vyjayanthi Chari	Related
Yuri Alexandrovich Bahturin	Related

G. Benkart, S. A. Lopes, and M. Ondrus: “A parametric family of subalgebras of the Weyl algebra, II: Irreducible modules,” pp. 73–98 in Recent developments in algebraic and combinatorial aspects of representation theory (12–16 August 2010, Bangalore, India and 18–20 May 2012, Riverside, CA). Edited by V. Chari, J. Greenstein, K. C. Misra, K. N. Raghavan, and S. Viswanath. Contemporary Mathematics 602. American Mathematical Society (Providence, RI), 2013. Part I was published in Trans. Am. Math. Soc. 367:3 (2015). Part III appeared as a 2014 preprint. MR 3203899 Zbl 1308.16022 ArXiv 1212.1404 incollection

An Ore extension over a polynomial algebra \( \mathbf{F}[x] \) is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra \( \mathbf{A}_h \) generated by elements \( x, y \), which satisfy \( yx - xy = h \), where \( h \in \mathbf{F}[x] \). When \( h \neq 0 \), these algebras are subalgebras of the Weyl algebra \( \mathbf{A}_1 \) and can be viewed as differential operators with polynomial coefficients. In previous work, we studied the structure of \( \mathbf{A}_h \) and determined its automorphism group \( \operatorname{Aut}_{\mathbb{F}}(\mathbf{A}_h) \) and the subalgebra of invariants under \( \operatorname{Aut}_{\mathbb{F}}(\mathbf{A}_h) \). Here we determine the irreducible \( \mathbf{A}_h \)-modules. In a sequel to this paper, we completely describe the derivations of \( \mathbf{A}_h \) over any field.

Samuel Antonio Lopes	Related
Kailash C. Misra	Related
Matthew Ondrus	Related
Vyjayanthi Chari	Related

@incollection {key3203899m,
	AUTHOR = {Benkart, Georgia and Lopes, Samuel A.
		 and Ondrus, Matthew},
	TITLE = {A parametric family of subalgebras of
		 the {W}eyl algebra, {II}: {I}rreducible
		 modules},
	BOOKTITLE = {Recent developments in algebraic and
		 combinatorial aspects of representation
		 theory},
	EDITOR = {Chari, Vyjayanthi and Greenstein, Jacob
		 and Misra, Kailash C. and Raghavan,
		 K. N. and Viswanath, Sankaran},
	SERIES = {Contemporary Mathematics},
	NUMBER = {602},
	PUBLISHER = {American Mathematical Society},
	ADDRESS = {Providence, RI},
	YEAR = {2013},
	PAGES = {73--98},
	DOI = {10.1090/conm/602/12027},
	NOTE = {(12--16 August 2010, Bangalore, India
		 and 18--20 May 2012, Riverside, CA).
		 Part I was published in \textit{Trans.
		 Am. Math. Soc.} \textbf{367}:3 (2015).
		 Part III appeared as a 2014 preprint.
		 ArXiv:1212.1404. MR:3203899. Zbl:1308.16022.},
	ISSN = {0271-4132},
	ISBN = {9780821890370},
}