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822.
Tomoyuki Shirai 《Transactions of the American Mathematical Society》2000,352(1):115-132
Let be an infinite -regular graph and its line graph. We consider discrete Laplacians on and , and show the exact relation between the spectrum of and that of . Our method is also applicable to -semiregular graphs, subdivision graphs and para-line graphs.
823.
Karel Dekimpe Veerle Ongenae 《Proceedings of the American Mathematical Society》2000,128(11):3191-3200
In this paper we prove that there are infinitely many abelian left symmetric algebras in dimensions . Equivalently this means that there are, up to affine conjugation, infinitely many simply transitive affine actions of , for . This is a result which is usually credited to A.T. Vasquez, but for which there is no proof in the literature.
824.
825.
826.
827.
In ([11]), we have studied quadratic Leibniz algebras that are Leibniz algebras endowed with symmetric, nondegenerate, and associative (or invariant) bilinear forms. The nonanticommutativity of the Leibniz product gives rise to other types of invariance for a bilinear form defined on a Leibniz algebra: the left invariance, the right invariance. In this article, we study the structure of Leibniz algebras endowed with nondegenerate, symmetric, and left (resp. right) invariant bilinear forms. In particular, the existence of such a bilinear form on a Leibniz algebra 𝔏 gives rise to a new algebra structure ☆ on the underlying vector space 𝔏. In this article, we study this new algebra, and we give information on the structure of this type of algebras by using some extensions introduced in [11]. In particular, we improve the results obtained in [22]. 相似文献
828.
Timothy Kohl 《代数通讯》2013,41(10):4290-4304
The holomorph of a group G is Norm B (λ(G)), the normalizer of the left regular representation λ(G) in its group of permutations B = Perm(G). The multiple holomorph of G is the normalizer of the holomorph in B. The multiple holomorph and its quotient by the holomorph encodes a great deal of information about the holomorph itself and about the group λ(G) and its conjugates within the holomorph. We explore the multiple holomorphs of the dihedral groups D n and quaternionic (dicyclic) groups Q n for n ≥ 3. 相似文献
829.
Zhixiang Wu 《代数通讯》2013,41(9):3869-3897
In the present article, we introduce G-graded left symmetric H-pseudoalgebras, where G is a grading group, and H is a cocommutative Hopf algebra. Some results about associative H-pseudoalgebras in [23] are generalized. The commutator algebras of the G-graded left symmetric H-pseudo-algebras are Lie H-pseudoalgebras, which are classified when the grading group is trivial in [3]. We investigate the left symmetric structure of Lie H-pseudoalgebras W(𝔟), S(𝔟), and He defined in [3]. 相似文献
830.
《代数通讯》2013,41(10):4899-4910
Abstract In this paper we show that a regular ring R is a generalized stable ring if and only if for every x ∈ R, there exist a w ∈ K(R) and a group G in R such that wx ∈ G. Also we show that if R is a generalized stable regular ring, then for any A ∈ M n (R), there exist right invertible matrices U 1, U 2 ∈ M n (R) and left invertible matrices V 1, V 2 ∈ M n (R) such that U 1 V 1 AU 2 V 2 = diag(e 1,…, e n ) for some idempotents e 1,…, e n ∈ R. 相似文献