The modular group algebra of an elementary abelian pgroup is isomorphic to the restricted enveloping algebra of a commutative restricted Lie algebra. The different ways of regarding this algebra result in different Hopf algebra structures that determine cup products on cohomology of modules. However, it is proved in this paper that the products with elements of the polynomial subring of the coh...

We present the surge of activity since 2005, around what we call the algebraic (as contrasted with the geometric) approach to Kazhdan’s property (T). The discussion includes also an announcement of a recent result (March 2006) regarding property (T) for linear groups over arbitrary finitely generated rings.

In this paper, we classify the derivations of degree-one generalized Weyl algebras over a univariate Laurent polynomial ring. particular, our results cover Weyl–Hayashi algebra, quantization first algebra arising as primitive factor [Formula: see text], and family which localize to group infinite with generators text] subject relation

The dichotomic physical quantities, also called propositions, can be naturally associated to maps of the set of states into the real interval [0,1]. We show that the structure of effect algebra associated to such maps can be represented by quasiring structures, which are a generalization of Boolean rings, in such a way that the ring operation of addition can be non-associative and the ring mult...

Let K be a field with char(K) 6= 2. Let us fix an algebraic closure Ka of K. Let us put Gal(K) := Aut(Ka/K). If X is an abelian variety of positive dimension over Ka then we write End(X) for the ring of all its Ka-endomorphisms and End (X) for the corresponding (semisimple finite-dimensional) Q-algebra End(X)⊗ Q. We write EndK(X) for the ring of all K-endomorphisms of X and End 0 K(X) for the c...

Abstract. Given a real hyperplane arrangement A, the complement M(A) of the complexification of A admits an action of the group Z2 by complex conjugation. We define the equivariant Orlik-Solomon algebra of A to be the Z2-equivariant cohomology ring of M(A) with coefficients in the field F2. We give a combinatorial presentation of this ring, and interpret it as a deformation of the ordinary Orli...

For a cancellative semigroup S and field F, it is proved that the algebra FS centrally essential if only group of fractions GS exists FGS essential. The has classical right ring which ring. There exist non-commutative algebras over fields zero characteristic (this contrasts with known fact are commutative).

It is shown that if the ring of constants of a restricted differential Lie algebra with a quasi-Frobenius inner part satisfies a polynomial identity (PI) then the original prime ring has a generalized polynomial identity (GPI). If additionally the ring of constants is semiprime then the original ring is PI. The case of a non-quasi-Frobenius inner part is also considered.