Compact cellular algebras and permutation groups

1999 ◽  
Vol 197-198 (1-3) ◽  
pp. 247-267 ◽  
Author(s):  
S Evdokimov
Keyword(s):  
Permutation Groups ◽  
Cellular Algebras

scholarly journals RELATIVE CELLULAR ALGEBRAS

2019 ◽  
Author(s):  
M. EHRIG ◽  
D. TUBBENHAUER
Keyword(s):  
Cellular Algebras

Standardly stratified algebras and cellular algebras

2002 ◽  
Vol 133 (1) ◽  
pp. 37-53 ◽  
Author(s):  
CHANGCHANG XI
Keyword(s):  
Projective Cover ◽  
Complete List ◽  
Injective Envelope ◽  
Finite Chain ◽  
Artin Algebra ◽  
Simple Modules ◽  
Cellular Algebras ◽  
Maximal Submodule ◽  
Standard Module ◽  
Composition Factors

Let A be an Artin algebra. Then there are finitely many non-isomorphic simple A-modules. Suppose S1, S2, …, Sn form a complete list of all non-isomorphic simple A-modules and we fix this ordering of simple modules. Let Pi and Qi be the projective cover and the injective envelope of Si respectively. With this order of simple modules we define for each i the standard module Δ(i) to be the maximal quotient of Pi with composition factors Sj with j [les ] i. Let Δ be the set of all these standard modules Δ(i). We denote by [Fscr ](Δ) the subcategory of A-mod whose objects are the modules M which have a Δ-filtration, namely there is a finite chain0 = M0 ⊂ M1 ⊂ M2 ⊂ … ⊂ Mt = Mof submodules of M such that Mi/Mi−1 is isomorphic to a module in Δ for all i. The modules in [Fscr ](Δ) are called Δ-good modules. Dually, we define the costandard module ∇(i) to be the maximal submodule of Qi with composition factors Sj with j [les ] i and denote by ∇ the collection of all costandard modules. In this way, we have also the subcategory [Fscr ](∇) of A-mod whose objects are these modules which have a ∇-filtration. Of course, we have the notion of ∇-good modules. Note that Δ(n) is always projective and ∇(n) is always injective.

scholarly journals JUCYS–MURPHY ELEMENTS AND CENTRES OF CELLULAR ALGEBRAS

2011 ◽  
Vol 85 (2) ◽  
pp. 261-270 ◽  
Author(s):  
YANBO LI
Keyword(s):  
Integral Domain ◽  
Sufficient Condition ◽  
Separation Condition ◽  
Symmetric Polynomials ◽  
Necessary And Sufficient Condition ◽  
Cellular Algebra ◽  
Cellular Basis ◽  
Cellular Algebras ◽  
Necessary And Sufficient

AbstractLet R be an integral domain and A a cellular algebra over R with a cellular basis {CλS,T∣λ∈Λ and S,T∈M(λ)}. Suppose that A is equipped with a family of Jucys–Murphy elements which satisfy the separation condition in the sense of Mathas [‘Seminormal forms and Gram determinants for cellular algebras’, J. reine angew. Math.619 (2008), 141–173, with an appendix by M. Soriano]. Let K be the field of fractions of R and AK=A⨂ RK. We give a necessary and sufficient condition under which the centre of AK consists of the symmetric polynomials in Jucys–Murphy elements. We also give an application of our result to Ariki–Koike algebras.

Affine cellular algebras and Morita equivalences

2014 ◽  
Vol 102 (4) ◽  
pp. 319-327 ◽  
Author(s):  
Guiyu Yang
Keyword(s):  
Cellular Algebras

Cellular algebras

1996 ◽  
Vol 123 (1) ◽  
pp. 1-34 ◽  
Author(s):  
J. J. Graham ◽  
G. I. Lehrer
Keyword(s):  
Cellular Algebras
Sign in / Sign up

Export Citation Format

Share Document