Multi-Matrix Models and Noncommutative Frobenius Algebras Obtained from Symmetric Groups and Brauer Algebras

The symmetric group and Brauer algebras

Brauer Algebras and the Brauer Group

An algebra is a vector space V over a field k together with a kbilinear product of vectors under which V is a ring. A certain class of algebras, called Brauer algebras algebras which split over a finite Galois extension appear in many subfields of abstract algebra, including K-theory and class field theory. Beginning with a definition of the the tensor product, we define and study Brauer algebr...

Noncommutative Symmetric Systems over Associative Algebras

This paper is the first of a sequence papers ([Z4]–[Z7]) on the NCS (noncommutative symmetric) systems over differential operator algebras in commutative or noncommutative variables ([Z4]); the NCS systems over the Grossman-Larson Hopf algebras ([GL], [F]) of labeled rooted trees ([Z6]); as well as their connections and applications to the inversion problem ([BCW], [E4]) and specializations of ...

Free quasi-symmetric functions and descent algebras for wreath products, and noncommutative multi-symmetric functions

Abstract. We introduce analogs of the Hopf algebra of Free quasi-symmetric functions with bases labelled by colored permutations. When the color set is a semigroup, an internal product can be introduced. This leads to the construction of generalized descent algebras associated with wreath products Γ ≀ Sn and to the corresponding generalizations of quasi-symmetric functions. The associated Hopf ...

Geometric Models for Noncommutative Algebras