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981.
Let H be a hereditary algebra of Dynkin type D n over a field k and 𝒞 H be the cluster category of H. Assume that n ≥ 5 and that T and T′ are tilting objects in 𝒞 H . We prove that the cluster-tilted algebra Γ = End𝒞 H (T)op is isomorphic to Γ′ = End𝒞 H (T′)op if and only if T = τ i T′ or T = στ j T′ for some integers i and j, where τ is the Auslander–Reiten translation and σ is the automorphism of 𝒞 H defined in Section 4. 相似文献
982.
In this article, we define a new associative dialgebra over a polynomial algebra F[x, y] with two indeterminates x and y. Left derivations, right derivations, derivations, and automorphisms of F[x, y] as associative dialgebra are determined. Meanwhile, we also determine all homogeneous derivations of F[x, y] as ?-graded Leibniz algebra, and automorphisms of Leibniz algebra F[x, y] preserving the standard filtration. 相似文献
983.
In this article, we propose an approach classifying a class of filiform Leibniz algebras. The approach is based on algebraic invariants. The method allows to classify all filiform Leibniz algebras (including filiform Lie algebras) in a given fixed dimensional case. 相似文献
984.
Atabey Kaygun 《代数通讯》2013,41(7):2513-2537
For module algebras and module coalgebras over an arbitrary bialgebra, we define two types of bivariant cyclic cohomology groups called bivariant Hopf cyclic cohomology and bivariant equivariant cyclic cohomology. These groups are defined through an extension of Connes' cyclic category Λ. We show that, in the case of module coalgebras, bivariant Hopf cyclic cohomology specializes to Hopf cyclic cohomology of Connes and Moscovici and its dual version by fixing either one of the variables as the ground field. We also prove an appropriate version of Morita invariance for both of these theories. 相似文献
985.
M. G. Mahmoudi 《代数通讯》2013,41(1):125-132
This is a variation on a theme of Bayer-Fluckiger, Shapiro, and Tignol related to hyperbolic involutions. More precisely, criteria for the hyperbolicity of involutions of quadratic extensions of simple algebras and involutions of the form σ ? τ and σ ? ρ, where σ is an involution of a central simple algebra A, τ is the nontrivial automorphism of a quadratic extension of the center of A, and ρ is an involution of a quaternion algebra are obtained. 相似文献
986.
Timur I. Nezhmetdinov 《代数通讯》2013,41(12):4669-4681
Let R be a finite commutative ring with identity and ? p d be the cyclic group of prime power order. Define R? p d to mean the group ring of ? p d over R. We determine the structure of the group of units of R? p d in the case when R is generated by an element whose order is not divisible by p. 相似文献
987.
Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities. 相似文献
988.
Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras, and Lie algebras. 相似文献
989.
In this article, the notion of universal enveloping algebra introduced in Ardizzoni [4] is specialized to the case of braided vector spaces whose Nichols algebra is quadratic as an algebra. In this setting, a classification of universal enveloping algebras for braided vector spaces of dimension not greater than 2 is handled. As an application, we investigate the structure of primitively generated connected braided bialgebras whose braided vector space of primitive elements forms a Nichols algebra, which is a quadratic algebra. 相似文献
990.