Z-graded identities of the Virasoro algebra

Author(s)

Fidelis, Claudemir ; Diniz, Diogo ; Koshlukov, Plamen

• Document type: Journal article
• Source: Journal of Algebra; v. 640, p. 31-pg., 2023-11-25.

Abstract

The Virasoro algebra, defined by the basis elements { Ln, c}n is an element of Z with commutation relations [Lm, Ln] = (m - n)Lm+n + delta m+n,0 center dot (Cmc) and [Lm, c] = 0, is an infinite-dimensional Lie algebra with many applications in various areas of Math-ematics and Theoretical Physics. Here the symbol delta i,j denotes the Kronecker delta and Cm = (m(m2 - 1))/12. This algebra admits a natural Z-grading. Over an infinite field of character-istic different from 2 and 3, we describe the graded identities of the Virasoro algebra for this grading. It turns out that all these Z-graded identities are consequences of a collection of polynomials of degree 2, 3 and 4 and that they do not admit a finite basis. (c) 2023 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 23/04011-9 - Struture of graded and/or trace algebras, and Invariant theory
• Grantee: Claudemir Fideles Bezerra Júnior
• Support Opportunities: Regular Research Grants
• FAPESP's process: 19/12498-0 - Graded polynomial identities and identity with trace, and invariant theory
• Grantee: Claudemir Fideles Bezerra Júnior
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants