共查询到20条相似文献,搜索用时 15 毫秒
1.
V. E. Govorov 《Mathematical Notes》1973,14(3):789-792
Let algebra R = Λ/P, where Λ is a free algebra over a field w. gl. dim R: = {min n ¦? R-modules X, Y, Tor n+1 R (X, Y)=0}. In order that w. gl. dim R≤2n (w. gl. dim R≤2n+1), it is necessary and sufficient that, for any two ideals of algebra Λ, a left ideal A and a right ideal B, containing ideal P, the following equation holds: $$AP^n \cap P^n B = AP^n B + P^{n + 1} (AP^n B \cap P^{n + 1} = AP^{n + 1} + P^{n + 1} B).$$ 相似文献
2.
Teng Xia Ju 《数学学报(英文版)》2009,25(5):831-844
In this paper, we show that if H is a finite-dimensional Hopf algebra such that H and H^* are semisimple, then gl.dim(A#σH)=gl.dim(A), where a is a convolution invertible cocycle. We also discuss the relationship of global dimensions between the crossed product A^#σH and the algebra A, where A is coacted by H. Dually, we give a sufficient condition for a finite dimensional coalgebra C and a finite dimensional semisimple Hopf algebra H such that gl.dim(C α H)=gl.dim(C). 相似文献
3.
We mainly study the global dimension of ω-smash coproducts. We show that if H is a Hopf algebra with a bijective antipode S H , and C ω ? H denotes the ω-smash coproduct, then gl.dim(C ω ? H) ≤ gl.dim(C) + gl.dim(H), where gl.dim(H) denotes the global dimension of H as a coalgebra. 相似文献
4.
Let R be a commutative ring with identity and I0 an ideal of R.We introduce and study the c-weak global dimension c-w.gl.dim(R/I0) of the factor ring R/I0.Let T be a w-linked extension of R,and we also introduce the wR-weak global dimension wR-w.gl.dim(T) of T.We show that the ring T with wR-w.gl.dim(T) =0 is exactly a field and the ring T with wR-w.gl.dim(T) ≤ 1 is exactly a PwRMD.As an application,we give an upper bound for the w-weak global dimension of a Cartesian square (RDTF,M).More precisely,if T is w-linked over R,then w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,c-w.gl.dim(D) + w-fdn D}.Furthermore,for a Milnor square (RDTF,M),we obtain w-w.gl.dim(R) ≤ max{wR-w.gl.dim(T) + w-fdR T,w-w.gl.dim(D) + w-fdR D}. 相似文献
5.
Let H be a Hopf k-algebra. We study the global homological dimension of the underlying coalgebra structure of H. We show that gl.dim(H) is equal to the injective dimension of the trivial right H-comodule k. We also prove that if D = C H is a crossed coproduct with invertible , then gl.dim(D) gl.dim(C) + gl.dim(H). Some applications of this result are obtained. Moreover, if C is a cocommutative coalgebra such that C
* is noetherian, then the global dimension of the coalgebra C coincides with the global dimension of the algebra C
*. 相似文献
6.
Let H be a finite-dimensional Hopf algebra and assume that both H and H* are semisimple.The main result of this paper is to show that the representation dimension is an invariant under cleft extensions of H,that is,rep.dim(A) = rep.dim(A# σ H).Some of the applications of this equality are also given. 相似文献
7.
Jia Gui ZHU 《数学学报(英文版)》2005,21(3):563-568
Let H be a finite dimensional cosemisimple Hopf algebra, C a left H-comodule coalgebra and let C = C/C(H^*)^+ be the quotient coalgebra and the smash coproduct of C and H. It is shown that if C/C is a eosemisimple coextension and C is an injective right C-comodule, then gl. dim(the smash coproduct of C and H) = gl. dim(C) = gl. dim(C), where gl. dim(C) denotes the global dimension of coalgebra C. 相似文献
8.
Hochschild (Co)Homology Dimension 总被引:3,自引:0,他引:3
In 1989 Happel asked the question whether, for a finite-dimensionalalgebra A over an algebraically closed field k, gl.dim A < if and only if hch.dim A < . Here, the Hochschild cohomologydimension of A is given by hch.dim A := inf{n N0 | dim HHi(A) = 0 for i > n}. Recently Buchweitz, Green, Madsen andSolberg gave a negative answer to Happel's question. They founda family of pathological algebras Aq for which gl.dim Aq = but hch.dim Aq = 2. These algebras are pathological in manyaspects. However, their Hochschild homology behaviors are notpathological any more; indeed one has hh.dim Aq = = gl.dimAq. Here, the Hochschild homology dimension of A is given byhh.dim A := inf{n N0 | dim HHi(A) = 0 for i > n}. This suggestsposing a seemingly more reasonable conjecture by replacing theHochschild cohomology dimension in Happel's question with theHochschild homology dimension: gl.dim A < if and only ifhh.dim A < if and only if hh.dim A = 0. The conjecture holdsfor commutative algebras and monomial algebras. In the casewhere A is a truncated quiver algebra, these conditions areequivalent to the condition that the quiver of A has no orientedcycles. Moreover, an algorithm for computing the Hochschildhomology of any monomial algebra is provided. Thus the cyclichomology of any monomial algebra can be read off when the underlyingfield is characteristic 0. 相似文献
9.
Stephen U. Chase 《代数通讯》2013,41(5):351-363
Let A be a commutative algebra over a field k, and VA be the k-subalgebra of Endk(A) generated by EndA(A) = A and all k-derivations of A. A study of the homological properties of VA was initiated by Hochschild, Kostant, and Rosenberg in [5], and continued by Rinehart [8], [9], Roos [11], Björk [1], Rinehart and Rosenberg [10], and others. It was proved in [5] that, if k is perfect and A is a regular affine algebra of dimension r, then the global dimension of VA is between r and 2r. Moreover, if k has positive characteristic, then gl.dim VA = 2r [8]. By a recent celebrated theorem of Roos [11], gl.dim VA = r if k has characteristic zero and A = k[x1, …, xr]; in this case VA is the so-called “Weyl algebra on 2r variables”. 相似文献
10.
We study possible values of the global dimension of endomorphism algebras of 2-term silting complexes. We show that for any algebra A whose global dimension gl.dim A ≤ 2 and any 2-term silting complex P in the bounded derived category D b (A) of A, the global dimension of \(\text {End}_{{D^b(A)}}(\mathbf {P})\) is at most 7. We also show that for each n > 2, there is an algebra A with gl.dim A = n such that D b (A) admits a 2-term silting complex P with \(\mathrm {gl. dim~}\text {End}_{{D^b(A)}}(\mathbf {P})\) infinite. 相似文献
11.
12.
Hermann Brune 《manuscripta mathematica》1978,26(1-2):141-154
13.
14.
给出二阶矩阵代数上保单位保Jordan半乘积数值半径的满映射的刻画以及保单位保Jor-dan半乘积交叉范数的满映射的刻画,补充完善了三阶以上矩阵代数的相应结果. 相似文献
15.
设B(H)是复Hilbert空间H上的有界线性算子全体且dim H≥2.本文证明了B(H)上的线性满射φ保持两个算子乘积非零投影性的充分必要条件是存在B(H)中的酉算子U以及复常数λ满足λ~2=1,使得φ(X)=λU~*XU,(?)X∈B(H).同时也得到了线性映射保持两个算子Jordan三乘积非零投影的充分必要条件. 相似文献
16.
研究了系数在模李超代数~$W(m,3,\underline{1})$
上的~$\frak{gl}(2,\mathbb{F})$ 的一维上同调, 其中~$\mathbb{F}$
是一个素特征的代数闭域且~$\frak{gl}(2,\mathbb{F})$
是系数在~$\mathbb{F}$ 上的~$2\times 2$ 阶矩阵李代数.
计算出所有~$\frak{gl}(2,\mathbb{F})$
到模李超代数~$W(m,3,\underline{1})$ 的子模的导子和内导子.
从而一维上同调~$\textrm{H}^{1}(\frak{gl}(2,\mathbb{F}),W(m,3,\underline{1}))$
可以完全用矩阵的形式表示. 相似文献
17.
18.
Muriel Livernet 《K-Theory》1999,18(4):317-337
We prove a analogous to Quillen's plus-construction in the category of algebras over an operad. For that purpose we prove that this category is a closed model category and prove the existence of an obstruction theory. We apply further this plus-construction for the specific cases of Lie algebras and Leibniz algebras which are a noncommutative version of Lie algebras: let sl(A) be the kernel of the trace map gl(A)A/[A,A], where A is an associative algebra with unit and gl(A) is the Lie algebra of matrices over A. Then the homotopy of slA)+ in the category of Lie algebras is the cyclic homology of A whereas it is the Hochschild homology of A in the category of Leibniz algebras. 相似文献
19.
G. I. Ol'shanskii 《Journal of Mathematical Sciences》1989,47(2):2466-2473
Starting from the universal enveloping algebras u(gl(n)), n=1,2,... we construct an algebra A, which gives a realization of the Yangian Y(gl(m)) and is a proper way to define the universal enveloping algebra for infinite-dimensional classical Lie algebras.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 142–150, 1987. 相似文献
20.
Vivek Sahai Shalini Srivastava 《Journal of Computational and Applied Mathematics》2003,160(1-2):271-281
The theory of irreducible p,q-representations of the complex Lie algebra gl(2) is developed. We construct a one variable model of irreducible p,q-representations of gl(2) in terms of p,q-derivative operator, and derive a generating function based on it. 相似文献