Two inequalities for parameters of a cellular algebra

1999 ◽  
Vol 96 (5) ◽  
pp. 3496-3504 ◽  
Author(s):  
S. A. Evdokimov ◽  
I. N. Ponomarenko
Keyword(s):  
Cellular Algebra

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.

When is a cellular algebra quasi-hereditary?

1999 ◽  
Vol 315 (2) ◽  
pp. 281-293 ◽  
Author(s):  
Steffen König ◽  
Changchang Xi
Keyword(s):  
Cellular Algebra

scholarly journals A Self-injective Cellular Algebra Is Weakly Symmetric

2000 ◽  
Vol 228 (1) ◽  
pp. 51-59 ◽  
Author(s):  
Steffen König ◽  
Changchang Xi
Keyword(s):  
Cellular Algebra ◽  
Weakly Symmetric

scholarly journals NAKAYAMA AUTOMORPHISMS OF FROBENIUS CELLULAR ALGEBRAS

2012 ◽  
Vol 86 (3) ◽  
pp. 515-524 ◽  
Author(s):  
YANBO LI
Keyword(s):  
Bilinear Form ◽  
Cellular Algebra ◽  
Cellular Basis ◽  
Finite Dimensional ◽  
Cellular Algebras ◽  
The Matrix ◽  
The Relationship

AbstractLet A be a finite-dimensional Frobenius cellular algebra with cell datum (Λ,M,C,i). Take a nondegenerate bilinear form f on A. In this paper, we study the relationship among i, f and a certain Nakayama automorphism α. In particular, we prove that the matrix associated with α with respect to the cellular basis is uni-triangular under a certain condition.

ON GRADED SYMMETRIC CELLULAR ALGEBRAS

2019 ◽  
Vol 108 (3) ◽  
pp. 349-362 ◽  
Author(s):  
YANBO LI ◽  
DEKE ZHAO
Keyword(s):  
Cellular Algebra ◽  
Finite Dimensional ◽  
Cellular Algebras

Let $A=\bigoplus _{i\in \mathbb{Z}}A_{i}$ be a finite-dimensional graded symmetric cellular algebra with a homogeneous symmetrizing trace of degree $d$. We prove that if $d\neq 0$ then $A_{-d}$ contains the Higman ideal $H(A)$ and $\dim H(A)\leq \dim A_{0}$, and provide a semisimplicity criterion for $A$ in terms of the centralizer of $A_{0}$.

On the number of cells of a cellular algebra

1999 ◽  
Vol 27 (11) ◽  
pp. 5463-5470 ◽  
Author(s):  
Steffen König ◽  
Changchang Xi
Keyword(s):  
Cellular Algebra ◽  
Number Of Cells

scholarly journals CENTRES OF SYMMETRIC CELLULAR ALGEBRAS

2010 ◽  
Vol 82 (3) ◽  
pp. 511-522 ◽  
Author(s):  
YANBO LI
Keyword(s):  
Integral Domain ◽  
Cellular Algebra ◽  
Cellular Basis ◽  
Cellular Algebras

AbstractLet R be an integral domain and A a symmetric cellular algebra over R with a cellular basis {CλS,T∣λ∈Λ,S,T∈M(λ)}. We construct an ideal L(A) of the centre of A and prove that L(A) contains the so-called Higman ideal. When R is a field, we prove that the dimension of L(A) is not less than the number of nonisomorphic simple A-modules.

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