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1.
The reciprocity relation of the Beta function is reformulated, and that of the Selberg function is presented.  相似文献   

2.
We study three different (co)homology theories for a family of pullbacks of algebras that we call oriented. We obtain a Mayer Vietoris long exact sequence of Hochschild and cyclic homology and cohomology groups for these algebras. We give examples showing that our sequence for Hochschild cohomology groups is different from the known ones. In case the algebras are given by quiver and relations, and that the simplicial homology and cohomology groups are defined, we obtain a similar result in a slightly wider context. Finally, we also study the fundamental groups of the bound quivers involved in the pullbacks.  相似文献   

3.
Yongjin Song 《K-Theory》1991,5(6):503-529
The main result of this paper is that there is, under a certain hypothesis, an isomorphism between the rational relative hermitian algebraic K-theory and the rational relative dihedral homology. The general line of the proof of the main theorem is an imitation of Goodwillie's paper, Relative algebraic K-theory and cyclic homology, but in a more complicated setting whose details require developing some new techniques. In the proof of the main theorem we use the hermitian Volodin model and some combinatorial calculations using the classical invariant theory of Loday and Procesi. We believe the computations used to prove the main result may be of independent interest.  相似文献   

4.
    
We compute the Hochschild cohomology and homology of the algebra Λ = kx, y〉/(x 2, xy + qyx, y 2) with coefficients in 1 Λψ for every degree preserving k-algebra automorphism ψ : Λ → Λ. As a result we obtain several interesting examples of the homological behavior of Λ as a bimodule.  相似文献   

5.
We present some basic identities for hypergeometric functions associatedwith the integrals of Euler type. We give a geometrical proof for formulaesuch as the identity between the single and double integrals expressingAppell's hypergeometric series F1 (a, b, b' c; x, y).  相似文献   

6.
《代数通讯》2013,41(3):1377-1386
Abstract

We introduce homology K-vector spaces with trivial coefficients for Leibniz n-algebras and we obtain exact sequences relating them. As a consequence we get a Hopf formula and several results on central extensions of Leibniz n-algebras.  相似文献   

7.
    
We define the Hochschild and cyclic (co)homology groups for superadditive categories and show that these (co)homology groups are graded Morita invariants. We also show that the Hochschild and cyclic homology are compatible with the tensor product of superadditive categories.  相似文献   

8.
    
Tomohiro Itagaki 《代数通讯》2017,45(5):2052-2073
Let K be an algebraically closed field and Γ a cyclic quiver. Xu and Wang investigated the Hochschild (co)homology groups of I, where I is an ideal of generated by one path. In this paper, in the case that I is an ideal of generated by two paths, we give the module structure of the Hochschild (co)homology groups of I.  相似文献   

9.
基于Cibils等人对单项式代数的向量空间Alt(DΛ)的组合描绘,得到了Fibonacci代数平凡扩张的一阶Hochschild上同调群的维数.  相似文献   

10.
    
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11.
    
Deke Zhao 《代数通讯》2013,41(11):4193-4201
It is shown that the Hochschild and cyclic (co)homology of superalgebras are graded equivalent invariants.  相似文献   

12.
Yunge Xu 《代数通讯》2013,41(1):115-131
The minimal projective bimodule resolutions of the exterior algebras are explicitly constructed. They are applied to calculate the Hochschild (co)homology of the exterior algebras. Thus the cyclic homology of the exterior algebras can be calculated in case the underlying field is of characteristic zero. Moreover, the Hochschild cohomology rings of the exterior algebras are determined by generators and relations.  相似文献   

13.
In this paper we prove the Lefschetz coincidence theorem in o-minimal expansions of fields using the o-minimal singular homology and cohomology.  相似文献   

14.
    
In this paper, we consider the module-relative-Hochschild homology and cohomology of tensor products of algebras and relate them to those of the factor algebras. Moreover, we show that the tensor product is formally smooth if and only if one of its factor algebras is formally smooth and the other is separable.  相似文献   

15.
Given a finite dimensional special biserial algebra A with normed basis we obtain the dimension formulae of the first Hochschild homology groups of A and the vector space Alt(DA). As a consequence, an explicit dimension formula of the first Hochschild cohomology group of trivial extension TA = A×DA in terms of the combinatorics of the quiver and relations is determined.  相似文献   

16.
In this paper, we consider the module-relative-Hochschild homology and cohomology under the ground ring extensions.  相似文献   

17.
We compute the homology of the Lie algebra W 1 of (polynomial) vector fields on the line with coefficients in symmetric powers of its adjoint representation. We also list the results obtained so far for the homology with coefficients in tensor powers and, in turn, use them for partially computing the homology of the Lie algebra of W 1-valued currents on the line.  相似文献   

18.
Let G be a second countable locally compact abelian group. The aim of this paper is to characterize the left translates on the Heisenberg group H(G) to be frames and Riesz bases in terms of the group Fourier transform.  相似文献   

19.
We describe a duality phenomenon for cohomology theories with the character of Gorenstein rings.  相似文献   

20.
Nonexistence of stable currents   总被引:1,自引:0,他引:1  
In this paper, we investigate nonexistence of stable integral currents in a compact hypersurface with positive Ricci curvature in a Euclidean spaceR m+1 and a vanishing theorem concerning the homology group is obtained.The project was supported by NNSFC, FECC and CPSF  相似文献   

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