Communications in Algebra

Xu, Xiaoping

doi: 10.1080/00927872.2014.918992pmid: N/A

We find a new representation of the simple Lie algebra of type E 7 on the polynomial algebra in 27 variables. Using this representation and Shen's idea of mixed product, we construct a new functor from E 6-Mod to E 7-Mod. A condition for the functor to map a finite-dimensional irreducible E 6-module to an infinite-dimensional irreducible E 7-module is obtained. Our general framework also gives a direct polynomial extension from irreducible E 6-modules to irreducible E 7-modules, which can be used to derive Gel'fand–Zetlin bases for E 7 from those for E 6 that can be obtained from those for D 5 according to our earlier work.

Le Boudec, Adrien

doi: 10.1080/00927872.2014.918994pmid: N/A

We compute the divergence of the finitely generated group SL n (𝒪𝒮), where 𝒮 is a finite set of valuations of a function field and 𝒪𝒮 is the corresponding ring of 𝒮-integer points. As an application, we deduce that all its asymptotic cones are without cut-points.

Grinshpon, S. Ya.; Nikolskaya, M. M.

doi: 10.1080/00927872.2014.918996pmid: N/A

We study primary Abelian groups containing proper fully invariant subgroup isomorphic to the group. The admissable sequence of the Ulm–Kaplansky invariants for primary groups is used. Using these sequences, IF-groups are described in some important classes of Abelian p-group.

Cui, Weideng

doi: 10.1080/00927872.2014.918997pmid: N/A

The modified quantized enveloping algebra has a remarkable canonical basis, which was introduced by Lusztig. In this paper, all these monomial elements of the canonical basis of for type A 2 are determined.

Fonseca, Andre

doi: 10.1080/00927872.2014.919300pmid: N/A

A categorical framework is provided, where most of the properties of the celebrated category 𝒪 (introduced by Bernstein, Gelfand, and Gelfand in [1]) are preserved but, for each simple object S, the dimension of Ext 1(S, S) no longer needs to be zero. A combinatorial description of such numbers is given and, consequently, a full description of all quivers corresponding to blocks of representations is obtained.

Àlvarez Montaner, Josep

doi: 10.1080/00927872.2014.923894pmid: N/A

We prove that sequentially Cohen–Macaulay rings in positive characteristic, as well as sequentially Cohen–Macaulay Stanley–Reisner rings in any characteristic, have trivial Lyubeznik table. Some other configurations of Lyubeznik tables are also provided depending on the deficiency modules of the ring.

Bemm, Laerte; Cortes, Wagner; Flora, Saradia Della; Ferrero, Miguel

doi: 10.1080/00927872.2014.923895pmid: N/A

In this paper we consider the transfer of the property of being a left Goldie ring between a ring A and its partial crossed product A*α G by a twisted partial action α of a group G on A.

Li, Zhi-Wei

doi: 10.1080/00927872.2014.923896pmid: N/A

Beligiannis and Marmaridis in 1994, constructed the one-sided triangulated structures on the stable categories of additive categories induced from some homologically finite subcategories. We extend their results to slightly more general settings. As an application of our results, we give some new examples of one-sided triangulated categories arising from abelian model categories. An interesting outcome is that we can describe the pretriangulated structures of the homotopy categories of abelian model categories via those of stable categories.

Zhang, Xiufu

doi: 10.1080/00927872.2014.923898pmid: N/A

We study the tensor product of a highest weight module with an intermediate series module over the Neveu–Schwarz algebra. If the highest weight module is nontrivial, the weight spaces of such a tensor product are infinite dimensional. We show that such a tensor product is indecomposable. Using a “shifting technique” developed by H. Chen, X. Guo, and K. Zhao for the Virasoro algebra case, we give necessary and sufficient conditions for such a tensor product to be irreducible. Furthermore, we give necessary and sufficient conditions for two such tensor products to be isomorphic.

Hou, Bo; Xu, Yuchun; Gao, Suogang

doi: 10.1080/00927872.2014.923899pmid: N/A

Let 𝕂 denote an algebraically closed field of characteristic zero. Let V denote a vector space over 𝕂 with finite positive dimension. By a Leonard triple on V, we mean an ordered triple of linear transformations A, A*, A ϵ in End(V) such that for each B ∈ {A, A*, A ϵ} there exists a basis for V with respect to which the matrix representing B is diagonal and the matrices representing the other two linear transformations are irreducible tridiagonal. The diameter of the Leonard triple (A, A*, A ϵ) is defined to be one less than the dimension of V. In this paper we define a family of Leonard triples said to be Bannai/Ito type and classify these Leonard triples with even diameters up to isomorphism. Moreover, we show that each of them satisfies the ℤ3-symmetric Askey–Wilson relations.