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《代数通讯》2013,41(5):2553-2567
ABSTRACT Let H be a Hopf algebra over a field k, and A a commutative right H-comodule algebra. This paper is concerned with homological algebra for Hopf modules. We investigate the projectivity, injectivity, and minimal injective resolutions of relative Hopf modules by using the functor HOM. 相似文献
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本文研究了D4 型量子包络代数的Gelfand-Kirillov 维数的计算问题. 利用文献[1] 中给出的Gelfand-Kirillov 维数的计算方法和文献[2] 中给出的D4 型量子包络代数的Groebner-Shirshov 基计算了D4型量子包络代数的Gelfand-Kirillov 维数, 得到的主要结果是D4 型量子包络代数的Gelfand-Kirillov 维数为28. 希望此结果为计算Dn型量子包络代数的Gelfand-Kirillov 维数提供一些思路. 相似文献
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《代数通讯》2013,41(12):5605-5630
We classify all total orders with a convex property on the positive root system of an arbitrary untwisted affine Lie algebra g. Such total orders are called convex orders and are used to construct convex bases of Poincaré-Birkhoff-Witt type of the upper triangular subalgebra Uq + of the quantized universal enveloping algebra Uq (g). 相似文献
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《Quaestiones Mathematicae》2013,36(4):475-477
Abstract Using the notion of a spectral set introduced by von-Neumann, we give some characterizations of C+ -algebras. Two conditions, each of which is necessary and sufficient for a Banach algebra to be uniform, are also obtained. 相似文献
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《代数通讯》2013,41(11):5179-5190
The semicentre of an arbitrary group algebra K[G] is studied. In particular necessary and sufficient conditions are shown such that the semicentre is equal to a fixed subring of K[Δ(G)]. Also the semicentre is always equal to a sum of centres of certain subgroup algebras. 相似文献
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《Quaestiones Mathematicae》2013,36(1-3):167-183
Abstract Since 1970 a number of operational quantities, characteristic of either the semi-Fredholm operators or of some “ideal” of compact-like operators, have been introduced in the theory of bounded operators between Banach spaces and applied successfully to for example perturbation theory. More recently such quantities have been introduced even in the abstract setting of Fredholm theory in a von Neumann algebra relative to some closed two-sided ideal. We show that in this fairly general setting there is only one “reasonable” set of such quantities—a result which in its present form is to the best of our knowledge new even in the case of B(H), the algebra of all bounded operators on a Hilbert space H. We accomplish this by first of all introducing the concept of a (reduced) minimum modulus in the setting of C*-algebras and developing the relevant techniques. In the process we generalise a result of Nikaido [N]. 相似文献
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《代数通讯》2013,41(11):5291-5305
Using equivalences of categories we provide general isomorphisms between the Brauer groups of different Hopf algebras. One of those is used to prove that the Brauer groups BC(k, H 4, rt ) for every dual quasitriangular structure rt on Sweedler's Hopf algebra H 4 are all isomorphic to the direct sum of (k, +) and the Brauer-Wall group of k. 相似文献
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In this paper the authors investigate the structure of the restricted Lie algebra cohomology of p-nilpotent Lie algebras with trivial p-power operation. Our study is facilitated by a spectral sequence whose E 2-term is the tensor product of the symmetric algebra on the dual of the Lie algebra with the ordinary Lie algebra cohomology and converges to the restricted cohomology ring. In many cases this spectral sequence collapses, and thus, the restricted Lie algebra cohomology is Cohen–Macaulay. A stronger result involves the collapsing of the spectral sequence and the cohomology ring identifying as a ring with the E 2-term. We present criteria for the collapsing of this spectral sequence and provide some examples where the ring isomorphism fails. Furthermore, we show that there are instances when the spectral sequence does not collapse and yields cohomology rings which are not Cohen-Macaulay. 相似文献
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本文研究了N(2,2,0)代数(S,*,△,0)的E-反演半群.利用N(2,2,0)代数的幂等元,弱逆元,中间单位元的性质和同宇关系,得到了N(2,2,0)代数的半群(S,*)构成E-反演半群的条件及元素α的右伴随非零零因子唯一,且为α的弱逆元等结论,这些结果进一步刻画了N(2,2,0)代数的结构. 相似文献
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Let H be a quasi-Hopf algebra, a weak Hopf algebra, or a braided Hopf algebra. Let B be an H-bicomodule algebra such that there exists a morphism of H-bicomodule algebras v: H → B. Then we can define an object Bco(H), which is a left-left Yetter–Drinfeld module over H, having extra properties that allow to make a smash product Bco(H)#H, which is an H-bicomodule algebra, isomorphic to B. 相似文献
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《代数通讯》2013,41(8):2809-2825
Let k be a field and An(ω) be the Taft's n2-dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D(An(ω)) of An(ω) is a ribbon Hopf algebra. In the previous articles, we constructed an n4-dimensional Hopf algebra Hn(p, q) which is isomorphic to D(An(ω)) if p ≠ 0 and q = ω?1 , and studied the irreducible representations of Hn(1, q) and the finite dimensional representations of H3(1, q). In this article, we examine the finite-dimensional representations of Hn(l q), equivalently, of D(An(ω)) for any n ≥ 2. We investigate the indecomposable left Hn(1, q)-module, and describe the structures and properties of all indecomposable modules and classify them when k is algebraically closed. We also give all almost split sequences in mod Hn(1, q), and the Auslander-Reiten-quiver of Hn(1 q). 相似文献
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《代数通讯》2013,41(8):2705-2711
Let A be a strong independence algebra of finite rank with at most one constant, and let G he the group of automorphisms of A. Let α be a singular endomorphism of αG = 〈{α} U G〉. We describe the elements of αG and give additional characterisations when A is a proper independence algebra and G is a periodic group. 相似文献
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《Quaestiones Mathematicae》2013,36(1-3):155-166
Abstract Let A be a von Neumann algebra on a Hilbert space H and let P(A) denote the projections of A. A comparative probability (CP) on A (or more correctly on P(A)) is a preorder ? on P(A) satisfying: 0 ? P ? P ε P(A) with Q ≠ 0 for some Q ε P(A). If P, Q ε P(A) then either P ? Q or Q ? P. If P, Q and R are all in P(A) and P⊥R, Q⊥R, then P ? Q ? P + R ? Q + R. Let τ be any of the usual locally convex topologies on A. We say ? is τ continuous if the interval topology induced on P(A) by ? is weaker than the τ topology on P(A). If μ an additive (completely additive) measure on P(A) then μ induces a uniformly (weakly) continuous CP ?μ on P(A) given by P ?μ Q if μ(P) ? μ(Q). We show that if A is the C* algebra C(H) of compact operators on an infinite dimensional Hilbert space H, the converse is true under an extra boundedness condition on the CP which is automatically satisfied whenever the identity is present in A = P(C(H)). 相似文献
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Julian D. Gilbey 《Journal of Algebraic Combinatorics》2004,19(1):25-45
We consider the permutation group algebra defined by Cameron and show that if the permutation group has no finite orbits, then no homogeneous element of degree one is a zero-divisor of the algebra. We proceed to make a conjecture which would show that the algebra is an integral domain if, in addition, the group is oligomorphic. We go on to show that this conjecture is true in certain special cases, including those of the form H Wr S and H Wr A, and show that in the oligormorphic case, the algebras corresponding to these special groups are polynomial algebras. In the H Wr A case, the algebra is related to the shuffle algebra of free Lie algebra theory. 相似文献
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《Quaestiones Mathematicae》2013,36(4):403-418
Abstract We find a necessary and sufficient condition on a Riesz space E such that a sub-Boolean algebra of components of a positive element generates the Boolean algebra of all components of the element. This condition yields a dual characterization of principal A-modules in the sense of D. Vuza. When applied to l-algebras, one finds improvements of results of J. Synnatzschke. 相似文献