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991.
Mateja Grašič 《Linear and Multilinear Algebra》2013,61(8):1007-1022
We show that the Lie algebra ? of skew-symmetric matrices with respect to either transpose or symplectic involution is zero product determined. This means that every bilinear map {·,·} from ? × ? into a vector space X is of the form {x, y} = T ([x, y]) for some linear map T provided that the following condition is fulfilled: [x, y] = 0 implies {x, y} = 0. 相似文献
992.
A particular orthogonal map on a finite-dimensional real quadratic vector space (V,?Q) with a non-degenerate quadratic form Q of any signature (p,?q) is considered. It can be viewed as a correlation of the vector space that leads to a dual Clifford algebra C?(V*,?Q) of linear functionals (multiforms) acting on the universal Clifford algebra C?(V,?Q). The map results in a unique involutive automorphism and a unique involutive anti-automorphism of C?(V,?Q). The anti-involution reduces to reversion (resp. conjugation) for any Euclidean (resp. anti-Euclidean) signature. When applied to a general element of the algebra, it results in transposition of the element matrix in the left regular representation of C?(V,?Q). We also give an example for real spinor spaces. The general setting for spinor representations will be treated in part II of this work [R. Ab?amowicz and B. Fauser, On the transposition anti-involution in real Clifford algebras II: Stabilizer groups of primitive idempotents, Linear Multilinear Algebra, to appear]. 相似文献
993.
We investigate indefinite higher-rank numerical ranges of a wide class of J-Hermitian matrices, J?=?I r ?⊕??I n?r , 0?<?r?<?n (A?∈?C n×n is said to be J-Hermitian if A?=?JA*J). Particular attention is paid to aspects of the theory that parallel the case of Hermitian matrices. 相似文献
994.
995.
David R. Wood 《Journal of Graph Theory》2013,73(3):318-321
The following theorem is proved: for all k‐connected graphs G and H each with at least n vertices, the treewidth of the cartesian product of G and H is at least . For , this lower bound is asymptotically tight for particular graphs G and H. This theorem generalizes a well‐known result about the treewidth of planar grid graphs. 相似文献
996.
997.
998.
Shuang-jian Guo 《代数通讯》2013,41(3):1025-1049
We first introduce the notion of partial group twisted smash product and construct a Morita context for partial coaction of co-Frobenius Hopf group coalgebra relating generalized partial group smash product and partial coinvariants. Furthermore, we study group-Galois extensions and reobtain some classical results in the partial case. Finally, we prove that any partial group Galois extension induces a unique partial group entwining map compatible with the partial right coaction. 相似文献
999.
Bálint Birszki 《代数通讯》2013,41(1):23-28
A permutation group G ≤ Sym(X) on a finite set X is sharp if |G|=∏ l?L(G)(|X| ? l), where L(G) = {|fix(g)| | 1 ≠ g ? G}. We show that no finite primitive permutation groups of twisted wreath type are sharp. 相似文献
1000.