Universität zu Köln

Molev, Alexander ORCID: 0000-0002-7321-1592 and Yakimova, Oksana (2019). QUANTISATION AND NILPOTENT LIMITS OF MISHCHENKO-FOMENKO SUBALGEBRAS. Represent. Theory, 23. S. 350 - 379. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 1088-4165

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Abstract

For any simple Lie algebra g and an element mu is an element of g*, the corresponding commutative subalgebra A(mu) of U(g) is defined as a homomorphic image of the Feigin-Frenkel centre associated with g. It is known that when mu is regular this subalgebra solves Vinberg's quantisation problem, as the graded image of A(mu) coincides with the Mishchenko-Fomenko subalgebra A (mu) over bar of S(g). By a conjecture of Feigin, Frenkel, and Toledano Laredo, this property extends to an arbitrary element mu. We give sufficient conditions on mu which imply the property. In particular, this proves the conjecture in type C and gives a new proof in type A(mu) We show that the algebra A(mu) is free in both cases and produce its generators in an explicit form. Moreover, we prove that in all classical types generators of A(mu) can be obtained via the canonical symmetrisation map from certain generators of (A) over bar mu. The symmetrisation map is also used to produce free generators of nilpotent limits of the algebras A(mu) and to give a positive solution of Vinberg's problem for these limit subalgebras.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Molev, Alexander UNSPECIFIED orcid.org/0000-0002-7321-1592 UNSPECIFIED Yakimova, Oksana UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-133497
DOI:	10.1090/ert/531
Journal or Publication Title:	Represent. Theory
Volume:	23
Page Range:	S. 350 - 379
Date:	2019
Publisher:	AMER MATHEMATICAL SOC
Place of Publication:	PROVIDENCE
ISSN:	1088-4165
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language UNIVERSAL ENVELOPING-ALGEBRAS; ARGUMENT SHIFT METHOD; LIE-ALGEBRAS; CENTRALIZERS; INDEX; REPRESENTATIONS; ORBITS; CONTRACTIONS; ELEMENTS Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/13349