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 $A_{0}$.

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.

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.

On derived equivalences and homological dimensions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ming Fang ◽  
Wei Hu ◽  
Steffen Koenig
Keyword(s):  
Global Dimension ◽  
Derived Categories ◽  
Lie Theory ◽  
Restriction Theorem ◽  
Dominant Dimension ◽  
Derived Equivalences ◽  
Finite Dimensional ◽  
Cellular Algebras ◽  
Homological Dimensions ◽  
Finite Dimensional Algebras

AbstractUnlike Hochschild (co)homology and K-theory, global and dominant dimensions of algebras are far from being invariant under derived equivalences in general. We show that, however, global dimension and dominant dimension are derived invariant when restricting to a class of algebras with anti-automorphisms preserving simples. Such anti-automorphisms exist for all cellular algebras and in particular for many finite-dimensional algebras arising in algebraic Lie theory. Both dimensions then can be characterised intrinsically inside certain derived categories. On the way, a restriction theorem is proved, and used, which says that derived equivalences between algebras with positive ν-dominant dimension always restrict to derived equivalences between their associated self-injective algebras, which under this assumption do exist.

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.

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

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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