Heisenberg-Virasoro代数的q-形变的量子群结构

构造了水平为零的扭的Heisenberg-Virasoro代数的一个q-形变Hvirq,证明它是一个quasi-hom-李代数.给出该代数的一个非平凡的量子群结构,即它是一个非交换且余交换的Hopf代数.     

The group algebra of the infinite symmetric group

The rational group algebra of the infinite symmetric group is studied using Young diagrams. Maximal and prime ideals are characterized and the maximal condition on ideals is proved. Research supported by the National Research Council of Canada.     

The Lie structure on the Hochschild cohomology of a modular group algebra

We prove that the Gerstenhaber bracket on the Hochschild cohomology of the group algebra of a cyclic group over a field of positive characteristic is not trivial. In this case, we relate the Lie algebra structure on the odd degrees of the Hochschild cohomology with a Witt-type algebra.     

The algebra of marriage: an episode in applied group theory

In 1949, André Weil contributed a mathematical appendix to Claude Lévi-Strauss's landmark book, The elementary structures of kinship. In this appendix, Weil (one of the Bourbaki mathematicians) used group-theoretic techniques to model Australian marriage systems. Weil's paper marked the beginning of mathematical anthropology. This essay describes Weil's analysis of marriage systems and traces the uneasy history of the application of group theory to kinship studies.     

The rational group algebra of a normally monomial group

In this paper, a complete irredundant set of a class of strong Shoda pairs of a finite group G is computed. The algebraic structure of the rational group algebra of a normally monomial group is thus obtained. A necessary and sufficient condition for G to be normally monomial is derived. The main result is also illustrated by computing a complete set of primitive central idempotents and the explicit Wedderburn decomposition of the rational group algebra of some normally monomial groups.     

On the first Hochschild cohomology group of an algebra

Let A≡KΔ /I be a factor of a path algebra. We develop a strategy to compute dim H ¹(A), the dimension of the first Hochschild cohomology group of A, using combinatorial data from (Δ,I). That allows us to connect dim H ¹(A) with the rank and p-rank of the fundamental group π₁(Δ,I) of (Δ,I). We get explicit formulae for dim H ¹(A), when every path in Δ parallel to an arrow belongs to I or when I is homogeneous. Received: 12 April 1999 / Revised version: 9 October 2000     

The hypercentral structure of the group of unitriangular automorphisms of a free metabelian Lie algebra

We describe the hypercentral structure of the group of unitriangular automorphisms of a free metabelian Lie algebra over an arbitrary field. Using it, we prove that this group admits no faithful representation by matrices over a field provided that the algebra rank is at least four.     

The alternative Clifford algebra of a ternary quadratic form

We prove that the alternative Clifford algebra of a nondegenerate ternary quadratic form is an octonion ring whose center is the ring of polynomials in one variable over the field of definition.     

The group of automorphisms of a commutative algebra

Author partially supported by the DGICYT (PB90-0300-C02-02)