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1.
Schur algebras of Brauer algebras are defined as endomorphism algebras of certain direct sums of ‘permutation modules’ over Brauer algebras. Explicit combinatorial bases of these new Schur algebras are given; in particular, these Schur algebras are defined integrally. The new Schur algebras are related to the Brauer algebra by Schur–Weyl dualities on the above sums of permutation modules. Moreover, they are shown to be quasi-hereditary. Over fields of characteristic different from two or three, the new Schur algebras are quasi-hereditary 1-covers of Brauer algebras, and hence the unique ‘canonical’ Schur algebras of Brauer algebras. 相似文献
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Zinbiel algebras were introduced by a way of Koszul dual to Leibniz algebras and connected with commutative associate algebras, pre-Lie algebras and dendriform algebras etc. In this article, the centroids of Zinbiel algebra are discussed. We study the proprieties of centroids and also determinate the centroids of Zinbiel algebras up to dimension ≤4. As consequent, we get the conclusion that the centroids of 2-dimensional Zinbiel algebras are not small and 3,4-dimensional Zinbiel algebras are almost small. 相似文献
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Abstract The question of existence of n-ary systems playing the role of enveloping algebras for Filippov (n-Lie) algebras is investigated. We consider the ternary algebras whose reduced binary algebras are associative, the associative algebras, and two other classes of ternary algebras as possible enveloping algebras. 相似文献
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V. V. Gorbatsevich 《Russian Mathematics (Iz VUZ)》2018,62(4):29-41
In this paper we introduce and study dual Lie algebras, i.e., Lie algebras over the algebra of dual numbers. We establish some fundamental properties of such Lie algebras and compare them with the corresponding properties of real and complex Lie algebras. We discuss the question of classification of dual Lie algebras of small dimension and consider the connection of dual Lie algebras with approximate Lie algebras. 相似文献
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The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras. The major conclusions contains the known results as special cases, e.g., that for path algebras over an algebraically closed field and for path algebras with relations from symmetrizable cartan matrices. Meanwhile, it means the corresponding results for some other important classes of algebras, that is, the path algebras of quivers over Frobenius algebras and the generalized path algebras endowed by Frobenius algebras at vertices. 相似文献
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本文构造了一类非Hopf 代数的双Frobenius 代数. 特别地, 在某些特殊的情形下, 这里构造的双Frobenius 代数是整体维数为3 的阶1 生成的Artin-Schelter 正则代数的Yoneda 代数. 相似文献
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Hartmann et al. defined the concept of cellularly stratified algebras that combine the features of both cellular algebras and stratified algebras. Many important diagram algebras in mathematics and physics, such as some Brauer, partition and BMW algebras, are cellularly stratified algebras, and each of these forms a tower of algebras. This article gives the concept of towers of cellularly stratified algebras in an axiomatic manner, and studies it in terms of induction and restriction functors. In particular, for certain towers of cellularly stratified algebras, we provide a criterion for semi-simplicity by using the cohomology groups of cell modules. 相似文献
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Jean A. Larson 《Algebra Universalis》1983,16(1):1-16
S. Ulam asked about the number of non-isomorphic projective algebras withk generators. This paper answers his question for projective algebras of finite dimension at least three and shows that there are the maximum possible number, continuum many, of non-isomorphic one-generated structures of finite dimensionn, wheren is at least three, of the following kinds: projective set algebras, projective algebras, diagonal-free cylindric set algebras, diagonal-free cylindric algebras, and cylindric algebras. 相似文献
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利用结合代数与n-李代数的张量积构造了一类无限维特征单的n-李代数,且证明了除n=3的情形以外,这类特征单n-李代数的内导子代数是特征单李代数. 相似文献
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In this paper, the double Ringel–Hall algebras of tame hereditary algebras are decomposed as the quantized enveloping algebras of the infinite-dimensional Lie algebras, which are the central extensions of the affine loop algebras and the infinite-dimensional Heisenberg algebras. The numbers of the generators of the Heisenberg algebras are explicitly given at each dimensional level. 相似文献
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Mathematische Zeitschrift - Diagram algebras, in particular Brauer algebras, Birman–Murakami-Wenzl algebras and partition algebras, are used in representation theory and invariant theory of... 相似文献
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In this paper, we study the structures of Clifford algebras. We represent the pinor and spinors spaces as subspaces of Clifford
algebras. With suitable bases of the Clifford algebras, we construct isomorphisms between Clifford algebras and matrix algebras.
In doing these we develop some spinor calculus. 相似文献
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N. G. Marchuk 《Russian Mathematics (Iz VUZ)》2018,62(11):23-27
Considering tensor products of special commutative algebras and general real Clifford algebras, we arrive at extended Clifford algebras. We have found that there are five types of extended Clifford algebras. The class of extended Clifford algebras is closed with respect to the tensor product. 相似文献
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研究了代数闭域K上三维非交换代数的分类.在已有三维交换代数分类的基础上,获得了代数闭域K上三维非交换代数A的分类,共有十二种类型.并且给出了非交换代数对应的路代数以及它们之间的一些关系. 相似文献
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M. Siles Molina 《Journal of Algebra》2008,319(12):5265-5278
Leavitt path algebras are shown to be algebras of right quotients of their corresponding path algebras. Using this fact we obtain maximal algebras of right quotients from those (Leavitt) path algebras whose associated graph satisfies that every vertex connects to a line point (equivalently, the Leavitt path algebra has essential socle). We also introduce and characterize the algebraic counterpart of Toeplitz algebras. 相似文献
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《Journal of Algebra》1997,190(2):372
The finite dimensional flexible composition algebras include the Hurwitz algebras (composition algebras with unit element), but also other interesting classes of algebras: the para-Hurwitz and the Okubo algebras. The above mentioned algebras present many symmetries, and this is reflected in their large derivation algebras. In the present paper we study the opposite question: What can be said about the composition algebras if we have some information about their derivation algebras? Our main result is the classification of all the composition algebras with such large derivation algebras. 相似文献
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José M. Pérez-Izquierdo 《Advances in Mathematics》2007,208(2):834-876
Sabinin algebras are a broad generalization of Lie algebras that include Lie, Malcev and Bol algebras as very particular examples. We present a construction of a universal enveloping algebra for Sabinin algebras, and the corresponding Poincaré-Birkhoff-Witt Theorem. A nonassociative counterpart of Hopf algebras is also introduced and a version of the Milnor-Moore Theorem is proved. Loop algebras and universal enveloping algebras of Sabinin algebras are natural examples of these nonassociative Hopf algebras. Identities of loops move to identities of nonassociative Hopf algebras by a linearizing process. In this way, nonassociative algebras and Hopf algebras interlace smoothly. 相似文献
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In this paper, we define a notion of AS-Gorenstein algebra for N-graded algebras, and show that symmetric AS-regular algebras of Gorenstein parameter 1 are exactly preprojective algebras of quasi-Fano algebras. This result can be compared with the fact that symmetric graded Frobenius algebras of Gorenstein parameter −1 are exactly trivial extensions of finite-dimensional algebras. The results of this paper suggest that there is a strong interaction between classification problems in noncommutative algebraic geometry and those in representation theory of finite-dimensional algebras. 相似文献