scholarly journals Recurrence relations in a modular representation algebra

1982 ◽  
Vol 26 (2) ◽  
pp. 215-219 ◽  
Author(s):  
J-C. Renaud
Keyword(s):  
Cyclic Group ◽  
Prime Order ◽  
Recurrence Relations ◽  
Binomial Coefficient ◽  
Modular Representation ◽  
Exterior Powers ◽  
Representation Algebra

In 1978 Almkvist and Fossum examined the decomposition of the exterior powers of basis modules in the modular representation algebra of a cyclic group of prime order. In particular they developed an isomorphism between these exterior powers and terms of binomial coefficient type in the algebra.We derive several recurrence relations for these terms.

scholarly journals On Modular Representation Algebras and a Class of Matrix Algebras

1982 ◽  
Vol 33 (3) ◽  
pp. 351-355 ◽  
Author(s):  
J-C. Renaud
Keyword(s):  
Tensor Product ◽  
Cyclic Group ◽  
Prime Order ◽  
Matrix Algebra ◽  
Modular Representation ◽  
Complex Field ◽  
Matrix Algebras ◽  
Direct Sum ◽  
Standard Operations

AbstractLet G be a cyclic group of prime order p and K a field of characteristic p. The set of classes of isomorphic indecomposable (K, G)-modules forms a basis over the complex field for an algebra p (Green, 1962) with addition and multiplication being derived from direct sum and tensor product operations.Algebras n with similar properties can be defined for all n ≥ 2. Each such algebra is isomorphic to a matrix algebra Mn of n × n matrices with complex entries and standard operations. The characters of elements of n are the eigenvalues of the corresponding matrices in Mn.

scholarly journals The characters and structure of a class of modular representation algebras of cyclic p-groups

1978 ◽  
Vol 26 (4) ◽  
pp. 410-418 ◽  
Author(s):  
J. C. Renaud
Keyword(s):  
Local Ring ◽  
Cyclic Group ◽  
Modular Representation ◽  
Alternative Proof ◽  
Local Rings ◽  
Prime Field ◽  
Direct Sum ◽  
Primitive Idempotents ◽  
C 30 ◽  
Representation Algebra

AbstractLet p,m be the modular representation algebra of the cyclic group of order pm over the prime field Zp. The characters of p, m are derived. For p = 2, this provides an alternative proof of a result due to Carlson (1975), tha 2,m is a local ring. It is shown that for p>2, p, m is a direct sum of 2m local rings. Their dimensions and primitive idempotents are derived.Subject classification (Amer. Math. Soc. (MOS) 1970): 20 C 20, 12 C 05, 12 C 30, 33 A 65.

scholarly journals Face Numbers and Nongeneric Initial Ideals

10.37236/1882 ◽  
2006 ◽  
Vol 11 (2) ◽  
Author(s):  
Eric Babson ◽  
Isabella Novik
Keyword(s):  
Cyclic Group ◽  
Simple Proof ◽  
Prime Order ◽  
Necessary Conditions ◽  
Betti Numbers ◽  
Proper Action ◽  
Initial Ideals ◽  
The Face ◽  
Algebraic Shifting

Certain necessary conditions on the face numbers and Betti numbers of simplicial complexes endowed with a proper action of a prime order cyclic group are established. A notion of colored algebraic shifting is defined and its properties are studied. As an application a new simple proof of the characterization of the flag face numbers of balanced Cohen-Macaulay complexes originally due to Stanley (necessity) and Björner, Frankl, and Stanley (sufficiency) is given. The necessity portion of their result is generalized to certain conditions on the face numbers and Betti numbers of balanced Buchsbaum complexes.

A Mapping Problem and Jp-Index. I

1970 ◽  
Vol 22 (4) ◽  
pp. 705-712 ◽  
Author(s):  
Masami Wakae ◽  
Oma Hamara
Keyword(s):  
Cyclic Group ◽  
Prime Order ◽  
Transformation Group ◽  
Classical Group ◽  
Cohomology Ring ◽  
Transformation Groups ◽  
Normal Space ◽  
Mapping Problem ◽  
Countable Basis ◽  
Kakutani Theorem

Indices of normal spaces with countable basis for equivariant mappings have been investigated by Bourgin [4; 6] and by Wu [11; 12] in the case where the transformation groups are of prime order p. One of us has extended the concept to the case where the transformation group is a cyclic group of order pt and discussed its applications to the Kakutani Theorem (see [10]). In this paper we will define the Jp-index of a normal space with countable basis in the case where the transformation group is a cyclic group of order n, where n is divisible by p. We will decide, by means of the spectral sequence technique of Borel [1; 2], the Jp-index of SO(n) where n is an odd integer divisible by p. The method used in this paper can be applied to find the Jp-index of a classical group G whose cohomology ring over Jp has a system of universally transgressive generators of odd degrees.

Reducibility for Non-Connected p-Adic Groups, With G° Of Prime Index

1995 ◽  
Vol 47 (2) ◽  
pp. 344-363 ◽  
Author(s):  
David Goldberg
Keyword(s):  
Cyclic Group ◽  
Prime Order ◽  
Discrete Series ◽  
Parabolic Subgroups ◽  
Orthogonal Groups ◽  
Definition Of

AbstractWe determine the structure of representations induced from discrete series of parabolic subgroups of quasi-split p-adic groups G with G/G° a cyclic group of prime order. We attach to each such representation an R-group which extends the definition of the Knapp-Stein R-group. We show that this R-group has the properties predicted by Arthur. We apply our results to the case of Orthogonal groups.

Modular Vector Invariants of Cyclic Permutation Representations

1999 ◽  
Vol 42 (1) ◽  
pp. 125-128 ◽  
Author(s):  
Larry Smith
Keyword(s):  
Prime Ideal ◽  
Cyclic Group ◽  
Finite Groups ◽  
Invariant Theory ◽  
Prime Order ◽  
Polynomial Algebra ◽  
Cyclic Permutation ◽  
Quotient Algebra ◽  
Chern Classes ◽  
Transfer Homomorphism

AbstractVector invariants of finite groups (see the introduction for an explanation of the terminology) have often been used to illustrate the difficulties of invariant theory in the modular case: see, e.g., [1], [2], [4], [7], [11] and [12]. It is therefore all the more surprising that the unpleasant properties of these invariants may be derived from two unexpected, and remarkable, nice properties: namely for vector permutation invariants of the cyclic group of prime order in characteristic p the image of the transfer homomorphism is a prime ideal, and the quotient algebra is a polynomial algebra on the top Chern classes of the action.

Actions of finite p-groups on homology manifolds

2001 ◽  
Vol 131 (3) ◽  
pp. 473-486 ◽  
Author(s):  
BERNHARD HANKE
Keyword(s):  
Fixed Point ◽  
Cyclic Group ◽  
Prime Order ◽  
Fixed Point Set ◽  
Poincare Duality ◽  
Cohomology Rings ◽  
Duality Space ◽  
Point Set ◽  
Homology Manifolds ◽  
Poincaré Duality Space

Let a cyclic group of odd prime order p act on a ℤ(p)-Poincaré duality space X. We prove a relation between the Witt classes associated to the [ ]p-cohomology rings of the fixed point set of this action and of X. This is applied to show a similar result for actions of finite p-groups on ℤ(p)-homology manifolds.

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