We study homological algebra in the abelian category Γ̃, whose objects are functors from finite pointed sets to vector spaces over Fp. The full calculation of Tor ∗ -groups between functors of degree not exceeding p is presented. We compare our calculations with known results on homology of symmetric groups, Steenrod algebra and functor homology computations in the abelian category F of functors...

Every AF-algebra A arises as the C *-algebra of a locally finite pointed directed graph in the sense of Kumjian, Pask, Raeburn, and Renault. For AF-algebras, the diagonal subalgebra defined by Strˇatilˇa and Voiculescu is consistent with Kumjian's notion of diagonal, and the groupoid arising from a well-chosen Bratteli diagram for A coincides with Kumjian's twist groupoid constructed from a dia...

This is a comment on the Kuranishi method of constructing analytic deformation spaces. It is based on a simple observation that the Kuranishi map can always be inverted in the category of L ∞-algebras. The L ∞-structure obtained by this inversion is used to define an " unobstructed " deformation functor which is always representable by a smooth pointed moduli space. The singular nature of the o...

In [8] de Concini, Kac and Procesi introduced the simply connected quantised universal enveloping algebra U = Uε,P (g) over C at a primitive lth root of unity ε associated to a simple finite-dimensional complex Lie algebra g. The importance of the study of the centre Z of U and its spectrum Maxspec(Z) is pointed out in [7,8]. In this article we consider the following two conjectures concerning ...

Let K be a (commutative) locally compact hypergroup with a left Haar measure. Let L1(K) be the hypergroup algebra of K and UCl(K) be the Banach space of bounded left uniformly continuous complex-valued functions on K. In this paper we show, among other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K.

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

The article presents computer algebra procedures and routines applied to the study of the Dirac field on curved spacetimes. The main part of the procedures is devoted to the construction of Pauli and Dirac matrices algebra on an anholonomic orthonormal reference frame. Then these procedures are used to compute the Dirac equation on curved spacetimes in a sequence of special dedicated routines. ...

Consider a bounded strongly pseudo-convex domain Ω with smooth boundary in Cn. Let T be the Toeplitz algebra on Bergman space La2(Ω). That is, is C⁎-algebra generated by operators {Tf:f∈L∞(Ω)}. Extending work [27], [28] special case of unit ball, we show that any such Ω, and {Tf:f∈VObdd}+K are essential commutants each other, where K collection compact On general considered this paper, proofs r...

Many very different themes could be used for a talk such as this one, but I have chosen von Neumann algebras because they are what led me into this circle of ideas. Thus the presentation will be historical rather than logical. A von Neumann algebra M is a *~algebra of bounded operators on a Hilbert space (Jf, ( , )) which contains the identity and is closed in the weak operator topology, i.e. i...

An action of a finite dimensional Hopf algebra H on a noncommutative associative algebra A is considered. Properties of A , the subalgebra of invariants in A, are studied. It is proved that if A is integral over Z(A), the centre of an algebra A, then A is integral over Z(A) H , the subalgebra of invariants in Z(A), for each of three cases: 1. the coradical H0 is cocommutative and char k = p > 0...