Conjugacy of Sylow 2-Subloops of the Chein Loops M 2n (G, 2)

In general, Sylow's Theorems do not hold for finite Moufang loops. It can be seen that if p is an odd prime then the Sylow p-subloops of the Chein loop M _2n (G, 2) are conjugate. Here we prove that it is also true that all the Sylow 2-subloops of M _2n (G, 2) are conjugate.     

Conjugacy Classes,Class Sums and Character Tables for Hopf Algebras

We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible left D(H)-modules. For quasitriangular semisimple Hopf algebras H, we prove that the product of two class sums is an integral combination of the class sums up to d ^?2 where d = dim H. We show also that in this case the character table is obtained from the S-matrix associated to D(H). Finally, we calculate explicitly the generalized character table of D(kS ₃), which is not a character table for any group. It moreover provides an example of a product of two class sums which is not an integral combination of class sums.     

Automating the Partition of Indexes

Abstract

In this article we show how attention to the structure of a particular algebraic calculation can lead to the simple implementation of powerful computer algebra tools. The creation of partitions for a set of indexes is required for the implementation of many theoretical structures. This may be difficult to do by hand even when the number of indexes is only moderately large. These partitions arise through the action of differentiation and so we mimic differentiation in a computer algebra package to create partitions of indexes. The strategies employed are extended to the creation of complementary set partitions, their reduction to equivalence classes, and the implementation of Edgeworth expansions and the exlog relations.     

Minimum Discrepancy Estimation in Probabilistic Knowledge Structures

Practical applications of the theory of knowledge structures often rely on a probabilistic version, known as the basic local independence model. The paper outlines various procedures for estimating its parameters, including maximum likelihood (ML) via the expectation-maximization (EM) algorithm, the computationally efficient minimum discrepancy (MD) estimation as well as MDML, a hybrid method combining the two approaches.     

On the Analytic Type of Artin Algebras

In this paper we give a complete analytic classification of Artin Gorenstein almost stretched algebras, i.e., Artin Gorenstein algebras with Hilbert function {1, n, 2,…, 2, 1,…, 1}.