On a class of algebras defined by partitions

Details On a class of algebras defined by partitions On a class of algebras defined by partitions

2002-10-14

arxiv.org/abs/math/0210195v1

Mathematics

Combinatorics

18 pages

Scientific paper

A class of associative (super) algebras is presented, which naturally generalize both the symmetric algebra $Sym(V)$ and the wedge algebra $\wedge (V)$, where $V$ is a vector-space. These algebras are in a bijection with those subsets of the set of the partitions which are closed under inclusions of partitions. We study the rate of growth of these algebras, then characterize the case where these algebras satisfy polynomial identities.

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