Brackets, superalgebras and spectral gap
type: Item
instance of: scholarly article
title: Brackets, superalgebras and spectral gap
zbMATH Open document ID: 1446.17034
author: Consuelo Martínez
author: E. Zelmanov
published in: São Paulo Journal of Mathematical Sciences
publication date: 2019-06-28T00:00:00Z
full work available at URL: http://hdl.handle.net/10651/51059
review text: The purpose of this survey is to discuss Poisson and contact brackets and related infinite-dimensional superalgebras. The authors started from the definition of Poisson and contact brackets on a commutative associative algebra, give some basic examples of Poisson and contact brackets, and formulate some open questions in Section 1. Section 2 is dedicated to superalgebras: definitions and examples; they talk about Kantor double process and Tits-Kantor-Koecher process. Later, in Section 3, they introduced superconformal algebras and gave the Kac-van de Leur's Conjecture. The next section is devoted to Harish-Chandra modules and spectral gaps. At the end of the paper, they discuss open questions.
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 17B63
Mathematics Subject Classification ID: 17C90
zbMATH DE Number: 7074582
zbMATH Keywords: bracket
zbMATH Keywords: superalgebra
zbMATH Keywords: conformal algebra
Wikidata QID: Q107721182
reviewed by: I. B. Kaĭgorodov
MaRDI profile type: Publication
OpenAlex ID: W2932694707
cites work: Theory of finite pseudoalgebras
cites work: Classification of irreducible representations of Lie algebra of vector fields on a torus
cites work: Classification of linearly compact simple Jordan and generalized Poisson superalgebras
cites work: A new \(N=6\) superconformal algebra
cites work: Vertex algebras associated with even lattices
cites work: Classification of finite simple Lie conformal superalgebras.
cites work: Lie superalgebras of string theories.
cites work: Lie superalgebras
cites work: Graded simple Jordan superalgebras of growth one
cites work: Q4940832
cites work: Q3215099
cites work: Q3975316
cites work: Q3717252
cites work: Imbedding of Jordan Algebras into Lie Algebras. I
cites work: Expander graphs in pure and applied mathematics
cites work: Specializations of Jordan Superalgebras
cites work: Representation theory of Jordan superalgebras I
cites work: Lie superalgebras graded by P ( n ) and Q ( n )
cites work: Classification of the indecomposable bounded admissible modules over the Virasoro Lie algebra with weightspaces of dimension not exceeding two
cites work: Simple finite-dimensional Jordan superalgebras of prime characteristic
cites work: Classification of Harish-Chandra modules over the Virasoro Lie algebra
cites work: Q3289051
cites work: Q5513844
DOI: 10.1007/S40863-019-00128-5
description: scientific article; zbMATH DE number 7074582