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31.
Itamar Stein 《代数通讯》2017,45(5):2105-2126
We give a new proof for the Littlewood-Richardson rule for the wreath product F?Sn where F is a finite group. Our proof does not use symmetric functions but use more elementary representation theoretic tools. We also derive a branching rule for inducing the natural embedding of F?Sn to F?Sn+1. We then apply the generalized Littlewood-Richardson rule for computing the ordinary quiver of the category F?FIn where FIn is the category of all injective functions between subsets of an n-element set. 相似文献
32.
David A. Towers 《代数通讯》2017,45(3):1284-1293
The purpose of this paper is to continue the study of chief factors of a Lie algebra and to prove a further strengthening of the Jordan–Hölder theorem for chief series. 相似文献
33.
In this paper, we determine the universal central extension, derivation algebra and automorphism group of the twisted N = 1 Schrödinger–Neveu–Schwarz algebra. Furthermore, we generalize these results to the generalized twisted N = 1 Schrödinger–Neveu–Schwarz algebra in the final section. 相似文献
34.
Brendan Dubsky 《代数通讯》2017,45(9):4084-4092
We prove Koszulity of certain linear path categories obtained from connected graphs with some infinite directed walk. These categories can be viewed as locally quadratic dual to preprojective algebras. 相似文献
35.
Diego Velasco 《代数通讯》2017,45(8):3610-3618
36.
We introduce a family of braided Hopf algebras that (in characteristic zero) generalizes the rank 1 Hopf algebras introduced by Krop and Radford and we study its cleft extensions. 相似文献
37.
We give an easier way to calculate a bijection from the set of isoclasses of tilted algebras of Dynkin type Δ to the set of configurations on the translation quiver ?Δ. 相似文献
38.
We investigate pointed Hopf algebras over finite nilpotent groups of odd order, with nilpotency class 2. For such a group G, we show that if its commutator subgroup coincides with its center, then there exists no non-trivial finite-dimensional pointed Hopf algebra with kG as its coradical. We apply these results to non-abelian groups of order p3, p4 and p5, and list all the pointed Hopf algebras of order p6, whose group of grouplikes is non-abelian. 相似文献
39.
Yafit Natani 《代数通讯》2017,45(9):3872-3885
In this paper, we investigate the basis graph of the monoid algebra of a submonoid of the monoid of mappings from N = {1,…,n} to itself, defined by a nested sequence of compositions of N. Each such monoid is a left regular band (LRB), that is, a semigroup S satisfying x2 = x and xyx = xy for all x,y∈S. This class is su?ciently rich that every path algebra of an acyclic quiver can be embedded in such a monoid algebra. The multiplication in the monoid algebra has a particularly simple quasi-multiplicative form, allowing definition over the integers. Combining this with a formula for Ext-groups for LRBs due to Margolis et al. [6], we get a simple criterion for the nested composition algebras to be hereditary. 相似文献
40.
Haicheng Zhang 《代数通讯》2017,45(3):1028-1036
We study the functorial properties of Bridgeland’s Hall algebras. Specifically, let 𝒜 and ? be two categories satisfying certain conditions for the definitions of Bridgeland’s Hall algebras, and let F:𝒜→? be a fully faithful exact functor, which preserves projectives, then F induces an embedding of algebras from the Bridgeland’s Hall algebra of 𝒜 to the one of ?. In addition, let A be a finite-dimensional algebra over a finite field and B some special quotient algebra of A, then the Bridgeland’s Hall algebra of B is the quotient algebra of the one of A. Moreover, we consider the BGP-reflection functors on the category of 2-cyclic complexes and obtain some homomorphisms of algebras among the subalgebras of Bridgeland’s Hall algebras. 相似文献