Zhu's algebras, C2-algebras and abelian radicals

Boris Feigin; Evgeny Feigin; Peter Littelmann

doi:https://doi.org/10.1016/j.jalgebra.2010.03.005

Zhu's algebras, C2-algebras and abelian radicals

Boris Feigin, Evgeny Feigin, Peter Littelmann

Research output: Contribution to journal › Article › peer-review

Abstract

This paper consists of three parts. In the first part we prove that Zhu's and C2-algebras in type A have the same dimensions. In the second part we compute the graded decomposition of the C2-algebras in type A, thus proving the Gaberdiel-Gannon conjecture. Our main tool is the theory of abelian radicals, which we develop in the third part.

Original language	English
Pages (from-to)	130-146
Number of pages	17
Journal	Journal of Algebra
Volume	329
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2010.03.005
State	Published - 1 Mar 2011
Externally published	Yes

Keywords

C2-algebra
Multiplicity free action
Spherical variety
Vertex operator algebra
Zhu's algebra

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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https://doi.org/10.1016/j.jalgebra.2010.03.005

Cite this

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title = "Zhu's algebras, C2-algebras and abelian radicals",

abstract = "This paper consists of three parts. In the first part we prove that Zhu's and C2-algebras in type A have the same dimensions. In the second part we compute the graded decomposition of the C2-algebras in type A, thus proving the Gaberdiel-Gannon conjecture. Our main tool is the theory of abelian radicals, which we develop in the third part.",

keywords = "C2-algebra, Multiplicity free action, Spherical variety, Vertex operator algebra, Zhu's algebra",

author = "Boris Feigin and Evgeny Feigin and Peter Littelmann",

note = "Funding Information: The work of E.F. was partially supported by the RFBR Grants 09-01-00058, 07-02-00799 and NSh-3472.2008.2, by Pierre Deligne fund based on his 2004 Balzan prize in mathematics and by Alexander von Humboldt Fellowship. The work of B.F. was partially supported by RFBR initiative interdisciplinary project 09-02-12446-ofi-m and by RFBR-CNRS grant 09-02-93106. The work of P.L. was partially supported by the priority program SPP 1377 of the German Science Foundation.",

year = "2011",

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doi = "https://doi.org/10.1016/j.jalgebra.2010.03.005",

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AU - Feigin, Boris

AU - Feigin, Evgeny

AU - Littelmann, Peter

N1 - Funding Information: The work of E.F. was partially supported by the RFBR Grants 09-01-00058, 07-02-00799 and NSh-3472.2008.2, by Pierre Deligne fund based on his 2004 Balzan prize in mathematics and by Alexander von Humboldt Fellowship. The work of B.F. was partially supported by RFBR initiative interdisciplinary project 09-02-12446-ofi-m and by RFBR-CNRS grant 09-02-93106. The work of P.L. was partially supported by the priority program SPP 1377 of the German Science Foundation.

PY - 2011/3/1

Y1 - 2011/3/1

N2 - This paper consists of three parts. In the first part we prove that Zhu's and C2-algebras in type A have the same dimensions. In the second part we compute the graded decomposition of the C2-algebras in type A, thus proving the Gaberdiel-Gannon conjecture. Our main tool is the theory of abelian radicals, which we develop in the third part.

AB - This paper consists of three parts. In the first part we prove that Zhu's and C2-algebras in type A have the same dimensions. In the second part we compute the graded decomposition of the C2-algebras in type A, thus proving the Gaberdiel-Gannon conjecture. Our main tool is the theory of abelian radicals, which we develop in the third part.

KW - C2-algebra

KW - Multiplicity free action

KW - Spherical variety

KW - Vertex operator algebra

KW - Zhu's algebra

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DO - https://doi.org/10.1016/j.jalgebra.2010.03.005

M3 - مقالة

SN - 0021-8693

VL - 329

SP - 130

EP - 146

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

Zhu's algebras, C2-algebras and abelian radicals

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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