scholarly journals Permutation centralizer algebras and multimatrix invariants

2016 ◽  
Vol 93 (6) ◽  
Author(s):  
Paolo Mattioli ◽  
Sanjaye Ramgoolam
Keyword(s):  
Centralizer Algebras

Operator Algebras with Contractive Approximate Identities

1994 ◽  
Vol 46 (2) ◽  
pp. 397-414 ◽  
Author(s):  
Yiu-Tung Poon ◽  
Zhong-Jin Ruan
Keyword(s):  
Operator Algebra ◽  
Operator Algebras ◽  
Banach Algebras ◽  
Approximate Identity ◽  
The Other ◽  
Double Centralizer ◽  
Approximate Identities ◽  
Centralizer Algebras ◽  
Matrix Norms ◽  
Centralizer Algebra

AbstractWe study operator algebras with contractive approximate identities and their double centralizer algebras. These operator algebras can be characterized as L∞- Banach algebras with contractive approximate identities. We provide two examples, which show that given a non-unital operator algebra A with a contractive approximate identity, its double centralizer algebra M(A) may admit different operator algebra matrix norms, with which M(A) contains A as an M-ideal. On the other hand, we show that there is a unique operator algebra matrix norm on the unitalization algebra A1 of A such that A1 contains A as an M-ideal.

THE KLEIN-4 DIAGRAM ALGEBRAS

2008 ◽  
Vol 07 (02) ◽  
pp. 231-262
Author(s):  
M. PARVATHI ◽  
B. SIVAKUMAR
Keyword(s):  
Bratteli Diagram ◽  
Permutation Representation ◽  
Signed Permutation ◽  
Permutation Module ◽  
New Class ◽  
Diagram Algebras ◽  
Irreducible Modules ◽  
Centralizer Algebras ◽  
Partition Algebras ◽  
Tensor Powers

In this paper we study a new class of diagram algebras, the Klein-4 diagram algebras denoted by Rk(n). These algebras are the centralizer algebras of the group Gn := (ℤ2 × ℤ2)≀Sn acting on V⊗k, where V is the signed permutation module for Gn These algebras have been realized as subalgebras of the extended G-vertex colored partition algebras introduced by Parvathi and Kennedy in [7]. In this paper we give a combinatorial rule for the decomposition of the tensor powers of the signed permutation representation of Gn by explicitly constructing the basis for the irreducible modules. In the process we also give the basis for the irreducible modules appearing in the decomposition of V⊗k in [5]. We then use this rule to describe the Bratteli diagram of Klein-4 diagram algebras.

scholarly journals A NEW PROOF OF THE FAITHFULNESS OF BRAUER'S REPRESENTATION OF TEMPERLEY–LIEB ALGEBRAS

2006 ◽  
Vol 16 (05) ◽  
pp. 959-968 ◽  
Author(s):  
KOSTA DOŠEN ◽  
ŽANA KOVIJANIĆ ◽  
ZORAN PETRIĆ
Keyword(s):  
Orthogonal Group ◽  
Group Case ◽  
Centralizer Algebras

The faithfulness of the orthogonal group case of Brauer's representation of the Brauer centralizer algebras restricted to their Temperley–Lieb subalgebras, which was established by Vaughan Jones, is here proved in a new, elementary and self-contained, manner.

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