THE CYCLIC AND SIMPLICIAL COHOMOLOGY OF THE BICYCLIC SEMIGROUP ALGEBRA

2010 ◽  
Vol 62 (3) ◽  
pp. 607-624 ◽  
Author(s):  
F. Gourdeau ◽  
M. C. White
Keyword(s):  
Semigroup Algebra ◽  
Bicyclic Semigroup

scholarly journals The C*-algebras of some inverse semigroups

1990 ◽  
Vol 42 (2) ◽  
pp. 335-348 ◽  
Author(s):  
Rachel Hancock ◽  
Iain Raeburn
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Algebra ◽  
Inverse Semigroups ◽  
Bicyclic Semigroup ◽  
C Algebras

We discuss the structure of some inverse semigroups and the associated C* algebras. In particular, we study the bicyclic semigroup and the free monogenic inverse semigroup, following earlier work of Conway, Duncan and Paterson. We then associate to each zero-one matrix A an inverse semigroup CA, and show that the C*-algebra OA of Cuntz and Krieger is closely related to the semigroup algebra C*(CA).

Inverse Subsemigroups of the Bicyclic Semigroup

2020 ◽  
Vol 108 (3-4) ◽  
pp. 550-556
Author(s):  
K. H. Hovsepyan
Keyword(s):  
Bicyclic Semigroup ◽  
Inverse Subsemigroups

scholarly journals Lebesgue Decomposition of Non-Commutative Measures

2020 ◽  
Author(s):  
Michael T Jury ◽  
Robert T W Martin
Keyword(s):  
Hilbert Space ◽  
Reproducing Kernel ◽  
Fock Space ◽  
Reproducing Kernel Hilbert Space ◽  
Semigroup Algebra ◽  
Space Theory ◽  
Lebesgue Decomposition ◽  
Sesquilinear Forms ◽  
Positive Linear Functionals ◽  
Algebra Theory

Abstract We extend the Lebesgue decomposition of positive measures with respect to Lebesgue measure on the complex unit circle to the non-commutative (NC) multi-variable setting of (positive) NC measures. These are positive linear functionals on a certain self-adjoint subspace of the Cuntz–Toeplitz $C^{\ast }-$algebra, the $C^{\ast }-$algebra of the left creation operators on the full Fock space. This theory is fundamentally connected to the representation theory of the Cuntz and Cuntz–Toeplitz $C^{\ast }-$algebras; any *−representation of the Cuntz–Toeplitz $C^{\ast }-$algebra is obtained (up to unitary equivalence), by applying a Gelfand–Naimark–Segal construction to a positive NC measure. Our approach combines the theory of Lebesgue decomposition of sesquilinear forms in Hilbert space, Lebesgue decomposition of row isometries, free semigroup algebra theory, NC reproducing kernel Hilbert space theory, and NC Hardy space theory.

scholarly journals Operator Algebras with Unique Preduals

2011 ◽  
Vol 54 (3) ◽  
pp. 411-421 ◽  
Author(s):  
Kenneth R. Davidson ◽  
Alex Wright
Keyword(s):  
Banach Space ◽  
Operator Algebra ◽  
Free Semigroup ◽  
Operator Algebras ◽  
Compact Operators ◽  
Semigroup Algebra ◽  
Dense Subalgebra

AbstractWe show that every free semigroup algebra has a (strongly) unique Banach space predual. We also provide a new simpler proof that a weak-∗ closed unital operator algebra containing a weak-∗ dense subalgebra of compact operators has a unique Banach space predual.

scholarly journals NORMAL DOMAINS WITH MONOMIAL PRESENTATIONS

2009 ◽  
Vol 19 (03) ◽  
pp. 287-303 ◽  
Author(s):  
ISABEL GOFFA ◽  
ERIC JESPERS ◽  
JAN OKNIŃSKI
Keyword(s):  
Commutative Algebra ◽  
Class Group ◽  
Semigroup Algebra ◽  
Closed Domain ◽  
Finitely Generated ◽  
Defining Relations ◽  
Integrally Closed ◽  
Algebra Over A Field

Let A be a finitely generated commutative algebra over a field K with a presentation A = K 〈X1,…, Xn | R〉, where R is a set of monomial relations in the generators X1,…, Xn. So A = K[S], the semigroup algebra of the monoid S = 〈X1,…, Xn | R〉. We characterize, purely in terms of the defining relations, when A is an integrally closed domain, provided R contains at most two relations. Also the class group of such algebras A is calculated.

Hausdorff topologies on the α-bicyclic semigroup

1987 ◽  
Vol 36 (1) ◽  
pp. 189-209
Author(s):  
J. W. Hogan
Keyword(s):  
Bicyclic Semigroup

Locally ample semigroup algebras

2014 ◽  
Vol 07 (04) ◽  
pp. 1450067 ◽  
Author(s):  
Xiaojiang Guo ◽  
K. P. Shum
Keyword(s):  
Semigroup Algebra ◽  
Semigroup Algebras ◽  
Abundant Semigroup ◽  
Ample Semigroup

An idempotent-connected abundant semigroup S is a locally ample semigroup if for any idempotent e of S, the local submonoid eSe of S is an ample subsemigroup of S. Clearly, an ample semigroup is a locally ample semigroup. In this paper, it is proved that the semigroup algebra of a finite locally ample semigroup is isomorphic to the semigroup algebra of an associate primitive abundant semigroup. As an application of this result, we characterize Jacobson radicals of finite locally ample semigroup algebras.

Johnson pseudo-contractibility of second duals of certain Banach algebras

2019 ◽  
pp. 2150012
Author(s):  
A. Sahami ◽  
E. Ghaderi ◽  
S. M. Kazemi Torbaghan ◽  
B. Olfatian Gillan
Keyword(s):  
Tensor Product ◽  
Matrix Algebra ◽  
Banach Algebras ◽  
Amenable Group ◽  
Semigroup Algebra ◽  
Archimedean Semigroup ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
The Matrix ◽  
Second Dual

In this paper, we study Johnson pseudo-contractibility of second dual of some Banach algebras. We show that the semigroup algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is a finite amenable group, where [Formula: see text] is an archimedean semigroup. We also show that the matrix algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is finite. We study Johnson pseudo-contractibility of certain projective tensor product second duals Banach algebras.

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