Search results for "REPRESENTATION"
showing 10 items of 1710 documents
Some geometric properties of disk algebras
2014
Abstract In this paper we study some geometrical properties of certain classes of uniform algebras, in particular the ball algebra A u ( B X ) of all uniformly continuous functions on the closed unit ball and holomorphic on the open unit ball of a complex Banach space X . We prove that A u ( B X ) has k -numerical index 1 for every k , the lushness and also the AHSP. Moreover, the disk algebra A ( D ) , and more in general any uniform algebra whose Choquet boundary has no isolated points, is proved to have the polynomial Daugavet property. Most of those properties are extended to the vector valued version A X of a uniform algebra A .
THE STRUCTURE OF MUTUALLY PERMUTABLE PRODUCTS OF FINITE NILPOTENT GROUPS
2007
We consider mutually permutable products G = AB of two nilpotent groups. The structure of the Sylow p-subgroups of its nilpotent residual is described.
On the structure of positive homomorphisms on algebras of real-valued continuous functions
2004
In this paper we study the structure of positive homomorphisms on real function algebras. We prove that every positive homomorphism is completely characterized by a family of sets and when the algebra is inverse-closed, by an ultrafilter of zero-sets of functions of the algebra. We show that the known sufficient conditions for every homomorphism of a real function algebra to be countably evaluating or a point evaluation are not necessary. Our results enable us to characterize the countably evaluating algebras as well as the Lindelof spaces as the spaces in which for every algebra, each countably evaluating homomorphism is a point evaluation.
Brauer characters and coprime action
2016
Abstract It is an open problem to show that under a coprime action, the number of invariant Brauer characters of a finite group is the number of the Brauer characters of the fixed point subgroup. We prove that this is true if the non-abelian simple groups satisfy a stronger condition.
Finite Groups with Only One NonLinear Irreducible Representation
2012
Let 𝕂 be an algebraically closed field. We classify the finite groups having exactly one irreducible 𝕂-representation of degree bigger than one. The case where the characteristic of 𝕂 is zero, was done by G. Seitz in 1968.
The structure of the state representation of shift invariant controllable and observable group codes
2000
AbstractIn this paper an investigation on the structure of the canonical trellis section of shift invariant, l-controllable and m-observable group codes is carried out. Necessary and sufficient conditions for a set of group homomorphisms in order that they represent the trellis section of this class of codes are established.
On the ∗-cocharacter sequence of 3×3 matrices
2000
Abstract Let M 3 (F) be the algebra of 3×3 matrices with involution * over a field F of characteristic zero. We study the ∗ -polynomial identities of M 3 (F) , where ∗=t is the transpose involution, through the representation theory of the hyperoctahedral group B n . After decomposing the space of multilinear ∗ -polynomial identities of degree n under the B n -action, we determine which irreducible B n -modules appear with non-zero multiplicity. In symbols, we write the nth ∗ -cocharacter χ n (M 3 (F),*)=∑ r=0 n ∑ λ⊢r,h(λ)⩽6 μ⊢n−r,h(μ)⩽3 m λ,μ χ λ,μ , where λ and μ are partitions of r and n−r , respectively, χ λ,μ is the irreducible B n -character associated to the pair (λ,μ) and m λ,μ ⩾0 i…
Ordinary and graded cocharacter of the Jordan algebra of 2x2 upper triangular matrices
2014
Abstract Let F be a field of characteristic zero and U J 2 ( F ) be the Jordan algebra of 2 × 2 upper triangular matrices over F . In this paper we give a complete description of the space of multilinear graded and ordinary identities in the language of Young diagrams through the representation theory of a Young subgroup of S n . For every Z 2 -grading of U J 2 ( F ) we compute the multiplicities in the graded cocharacter sequence and furthermore we compute the ordinary cocharacter.
Transportation cost inequalities on path and loop groups
2005
AbstractLet G be a connected Lie group with the Lie algebra G. The action of Cameron–Martin space H(G) on the path space Pe(G) introduced by L. Gross (Illinois J. Math. 36 (1992) 447) is free. Using this fact, we define the H-distance on Pe(G), which enables us to establish a transportation cost inequality on Pe(G). This method will be generalized to the path space over the loop group Le(G), so that we obtain a transportation cost inequality for heat measures on Le(G).
Analysis of properties of recombination operators proposed for the node-depth encoding
2011
The node-depth encoding is a representation for evolutionary algorithms applied to tree problems. Its represents trees by storing the nodes and their depth in a proper ordered list. The original formulation of the node-depth encoding has only mutation operators as the search mechanism. Although it is computationally efficient, the exclusive use of mutation restricts the exploration of the search space and the algorithm convergence. Then, this work proposes two specific recombination operators to improve the convergence of the algorithm using the node-depth encoding representation. These operators are based on recombination operators for permutation representations. Analysis of the proposed …