Odd family algebras

Abstract

A new class of associative algebras related to simple complex Lie algebras (or root systems) was introduced and studied in [K1] and [K2]. They were named classical and quantum family algebras. The aim of this paper is to introduce the odd analogue of these algebras and expose some results about their structure. In particular, we describe the structure of g-module Λ(g) and compute the odd exponents for some cases.