Hochschild cohomology of truncated quiver algebras

For a truncated quiver algebra over a field of an arbitrary characteristic, its Hochschild cohomology is calculated. Moreover, it is shown that its Hochschild cohomology algebra is finitedimensional if and only if its global dimension is finite if and only if its quiver has no oriented cycles.     

Hochschild cohomology of special biserial algebras

Based on a four-term exact sequence,the formulae on the dimensions of the first and the second Hochschild cohomology groups of special biserial algebras with normed bases are obtained in terms of combinatorics.     

Cyclic cohomology of certain nuclear Fréchet algebras and DF algebras

We give explicit formulae for the continuous Hochschild and cyclic homology and cohomology of certain \(\hat \otimes\)-algebras. We use well-developed homological techniques together with some niceties of the theory of locally convex spaces to generalize the results known in the case of Banach algebras and their inverse limits to wider classes of topological algebras. To this end we show that, for a continuous morphism ?: x → y of complexes of complete nuclear DF-spaces, the isomorphism of cohomology groups H ⁿ(?): H ⁿ (x) → H ⁿ (y) is automatically topological. The continuous cyclic-type homology and cohomology are described up to topological isomorphism for the following classes of biprojective \(\hat \otimes\)-algebras: the tensor algebra E \(\hat \otimes\) F generated by the duality (E,F,<·,·>) for nuclear Fréchet spaces E and F or for nuclear DF-spaces E and F; nuclear biprojective Köthe algebras λ(P) which are Fréchet spaces or DF-spaces; the algebra of distributions ε^*(G) on a compact Lie group G.     

Entire cyclic cohomology of ?/2-graded banach algebras

We extend A. Connes' theory of entire cyclic cohomology to /2-graded Banach algebras.Laboratoire propre du CNRS LP 7061.     

Gelfand�CTsetlin algebras and cohomology rings of Laumon spaces

Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GL _n . We calculate the equivariant cohomology rings of the Laumon moduli spaces in terms of Gelfand–Tsetlin subalgebra of U(gl _n ) and formulate a conjectural answer for the small quantum cohomology rings in terms of certain commutative shift of argument subalgebras of U(gl _n ).     

The cohomology group of weak entwining structure

In this paper, we reveal that a weak entwining structure admits a rich cohomology theory. As an application we compute the cohomology of a weak entwining structure associated to a weak coalgebra-Galois extension.     

A super Frobenius formula for the characters of Iwahori–Hecke algebras

In this article, we establish a super Frobenius formula for the characters of Iwahori–Hecke algebras. We define Hall–Littlewood supersymmetric functions in a standard manner to make supersymmetric functions from symmetric functions, and give some properties of supersymmetric functions. Based on Schur–Weyl reciprocity between Iwahori–Hecke algebras and the general quantum super algebras, which was obtained in Mitsuhashi [H. Mitsuhashi, Schur–Weyl reciprocity between the quantum superalgebra and the Iwahori–Hecke algebra, Algeb. Represent. Theor. 9 (2006), pp. 309–322.], we derive that the Hall–Littlewood supersymmetric functions, up to constant, generates the values of the irreducible characters of Iwahori–Hecke algebras at the elements corresponding to cycle permutations. Our formula in this article includes both the ordinary quantum case that was obtained in Ram [A. Ram, A Frobenius formula for the characters of the Hecke algebra, Invent. Math. 106 (1991), pp. 461–488.] and the classical super case.     

The automorphisms of Petit’s algebras

Let σ be an automorphism of a field K with fixed field F. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras K[t;σ]∕fK[t;σ] obtained when the twisted polynomial f∈K[t;σ] is invariant, and were first defined by Petit. We compute all their automorphisms if σ commutes with all automorphisms in Aut_F(K) and n≥m?1, where n is the order of σ and m the degree of f, and obtain partial results for n<m?1. In the case where K∕F is a finite Galois field extension, we obtain more detailed information on the structure of the automorphism groups of these nonassociative unital algebras over F. We also briefly investigate when two such algebras are isomorphic.     

The K-theoretical range of Cuntz–Krieger algebras

We augment Restorff's classification of purely infinite Cuntz–Krieger algebras by describing the range of his invariant on purely infinite Cuntz–Krieger algebras. We also describe its range on purely infinite graph C^?$C^{?}$-algebras with finitely many ideals, and provide ‘unital’ range results for purely infinite Cuntz–Krieger algebras and unital purely infinite graph C^?$C^{?}$-algebras.     

The classification of N-dimensional non-associative Jordan algebras with (N − 3)-dimensional annihilator

The paper is devoted to give a complete classification of all n-dimensional non-associative Jordan algebras with (n?3)-dimensional annihilator over an algebraically closed field of characteristic ≠2. We also give a complete classification of all n-dimensional Jordan algebras with (n?1)- and (n?2)-dimensional annihilator.     

The Semigroup Characterizations of Positive Implicative BCK—algebras

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＢｙａＢＣＩ－ａｌｇｅｂｒａｗｅｍｅａｎａｎａｌｇｅｂｒａ（Ｘ，，０）ｏｆｔｙｐｅ（２，０）ｗｉｔｈｔｈｅｆｏｌｌｏｗｉｎｇｃｏｎｄｉ－ｔｉｏｎｓ：（１）（（ｘｙ）（ｘｚ））（ｚｙ）＝０；（２）（ｘ（ｘｙ））ｙ＝０；（３）ｘｘ＝０；（４）ｘｙ＝ｙｘ＝０ｉｍｐｌｉｅｓｘ＝ｙ．ＩｆａＢＣＩ－ａｌｇｅｂｒａ（Ｘ，，０）ｓａｔｉｓｆｉｅｓ（５）０ｘ＝０．ｔｈｅｎｉｔｉｓｃａｌｌｅｄａＢＣＫ－ａｌｇｅｂｒａ．ＩｎａＢＣＩ－ａｌｇｅｂｒａ，ｔｈｅｆ…     

The first moment of Salié sums

The main objective of this article is to study the asymptotic behavior of Salié sums over arithmetic progressions. We deduce from our asymptotic formula that Salié sums possess a bias towards being positive. The method we use is based on the Kuznetsov formula for modular forms of half-integral weight. Moreover, in order to develop an explicit formula, we are led to determine an explicit orthogonal basis of the space of modular forms of half-integral weight.     

The Chen–Ruan cohomology of moduli of curves of genus 2 with marked points

In this work we describe the Chen–Ruan cohomology of the moduli stack of smooth and stable genus 2 curves with marked points. In the first half of the paper we compute the additive structure of the Chen–Ruan cohomology ring for the moduli stack of stable n-pointed genus 2 curves, describing it as a rationally graded vector space. In the second part we give generators for the even Chen–Ruan cohomology ring as an algebra on the ordinary cohomology.     

The topological center of the spectrum of some distal algebras

The topological center of the spectrum of the Weyl algebra W, i.e. the norm closure of the algebra generated by the set of functions , is characterized in a recent paper by Jabbari and Namioka (Ellis group and the topological center of the flow generated by the map , to appear in Milan J. Math.). By the techniques essentially used in the cited paper, the topological center of the spectrum of the subalgebra W _k , the norm closure of the algebra generated by the set of functions , will be characterized, for all k∈ℕ. Also an example of a non-minimal dynamical system, with the enveloping semigroup Σ, for which the set of all continuous elements of Σ is not equal to the topological center of Σ, is given.     

The actions ofS n+1 andS n on the cohomology ring of a coxeter arrangement of typeA n−1

Let be the complexified Coxeter arrangement of hyperplanes of typeA _n−1. In this paper we construct anS _n+1 extension of the naturalS _n action on the complex cohomology ring of the complement ofA _n−1. Recurrence formulas connecting characters with respect to theS _n and theS _n+1 action are given.     

Two-Loop β-Function of N = 1 Supersymmetric Quantum Electrodynamics Regularized Using Higher Covariant Derivatives

We calculate the two-loop -function of the N=1 supersymmetric electrodynamics regularized using the method of higher covariant derivatives. We show that this function coincides with the result obtained using the dimensional reduction method for any form of the regularizing term.     

Two-Loop Anomalous Dimension of N = 1 Supersymmetric Quantum Electrodynamics Regularized Using Higher Covariant Derivatives

We calculate the two-loop anomalous dimension in the N=1 supersymmetric electrodynamics regularized through the higher covariant derivative method using the minimum subtraction scheme and show that the result is independent of the form of the regularizing term but does depend on the ratio between the masses M of the Pauli–Villars fields and the dimensional constant in the regularizing term. We propose a simple subtraction scheme in which the result is independent of the parameters of the regularization used.