In this paper, a semigroup algebra consisting of polynomial expressions with coefficients in field F and exponents an additive submonoid M Q≥0 is called Puiseux denoted by F[M]. Here we study the atomic structure algebras. To begin with, answer isomorphism problem for class algebras, that is, show if two algebras F[M1] F[M2] are isomorphic, then monoids M1 M2 must be isomorphic. Then construct ...

Ultragraphs give rise to labelled graphs. We realize algebras associated such graphs as groupoid algebras, generalizing a known algebra realization of ultragraph C*-algebras any ultragraph. Then, we characterize the shift space an tight spectrum inverse semigroup with via its graph. In purely algebraic setting, show that partial action used describe Leavitt path skew group ring is equivalent du...

This paper addresses extensions of the complex Ornstein-Uhlenbeck semigroup to operator algebras in free probability theory. If a1, . . . , ak are ∗-free R-diagonal operators in a II1 factor, then Dt(ai1 · · · ain) = e −ntai1 · · · ain defines a dilation semigroup on the non-self-adjoint operator algebra generated by a1, . . . , ak. We show that Dt extends (in two different ways) to a semigroup...

There is a well-known combinatorial definition, based on ordered set partitions, of the semigroup of faces of the braid arrangement. We generalize this definition to obtain a semigroup ΣGn associated with G ≀ Sn, the wreath product of the symmetric group Sn with an arbitrary group G. Techniques of Bidigare and Brown are adapted to construct an anti-homomorphism from the Sn-invariant subalgebra ...