Brackets, superalgebras and spectral gap (Q2000117)

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.