共查询到20条相似文献,搜索用时 46 毫秒
1.
Caio De Naday Hornhardt Helen Samara Dos Santos Mikhail Kochetov 《Journal of Pure and Applied Algebra》2019,223(4):1590-1616
We classify gradings by arbitrary abelian groups on the classical simple Lie superalgebras , , and on the simple associative superalgebras , , over an algebraically closed field: fine gradings up to equivalence and G-gradings, for a fixed group G, up to isomorphism. As a corollary, we also classify up to isomorphism the G-gradings on the classical Lie superalgebra that are induced from G-gradings on . In the case of Lie superalgebras, the characteristic is assumed to be 0. 相似文献
2.
《Discrete Mathematics》2022,345(7):112886
In this article we investigate a problem in graph theory, which has an equivalent reformulation in extremal set theory similar to the problems researched in “A general 2-part Erd?s-Ko-Rado theorem” by Gyula O.H. Katona, who proposed our problem as well. In the graph theoretic form we examine the clique number of the Xor product of two isomorphic Kneser graphs. Denote this number with . We give lower and upper bounds on , and we solve the problem up to a constant deviation depending only on k, and find the exact value for if N is large enough. Also we compute that is asymptotically equivalent to . 相似文献
3.
We construct a minimal free resolution of the semigroup ring in terms of minimal resolutions of and when is a numerical semigroup obtained by gluing two numerical semigroups and . Using our explicit construction, we compute the Betti numbers, graded Betti numbers, regularity and Hilbert series of , and prove that the minimal free resolution of has a differential graded algebra structure provided the resolutions of and possess them. We discuss the consequences of our results in small embedding dimensions. Finally, we give an extension of our main result to semigroups in . 相似文献
4.
5.
6.
《Discrete Mathematics》2022,345(5):112786
Let G be a connected graph with vertices and edges. The nullity of G, denoted by , is the multiplicity of eigenvalue zero of the adjacency matrix of G. Ma, Wong and Tian (2016) proved that unless G is a cycle of order a multiple of 4, where is the elementary cyclic number of G and is the number of leaves of G. Recently, Chang, Chang and Zheng (2020) characterized the leaf-free graphs with nullity , thus leaving the problem to characterize connected graphs G with nullity when . In this paper, we solve this problem completely. 相似文献
7.
8.
9.
《Discrete Mathematics》2022,345(10):112998
Let G be a graph and let f be a positive integer-valued function on . In this paper, we show that if for all , , then G has a spanning tree T containing an arbitrary given matching such that for each vertex v, , where denotes the number of components of and denotes the number of components of the induced subgraph with the vertex set S. This is an improvement of several results. Next, we prove that if for all , , then G admits a spanning closed walk passing through the edges of an arbitrary given matching meeting each vertex v at most times. This result solves a long-standing conjecture due to Jackson and Wormald (1990). 相似文献
10.
In this paper we construct a ring A which has annihilator condition (a.c.) and we show that neither nor has this property. This answers in negative a question asked by Hong, Kim, Lee and Nielsen. We also show that there is an algebra A which does not have annihilator condition while both and have this property. 相似文献
11.
Quotients of Banach-Lie groups are regarded as topological groups with Lie algebra in the sense of Hofmann-Morris on the one hand, and as Q-groups in the sense of Barre-Plaisant on the other hand. For the groups of the type where is a pseudo-discrete normal subgroup, their Lie algebra in the sense of Q-groups turns out to be isomorphic to the Lie algebra of G, which is in general merely a dense subalgebra of the Lie algebra of when regarded as a topological group with Lie algebra. The submersion-like behavior of quotient maps of Banach-Lie groups is also investigated. The two aforementioned approaches to the Lie theory of the quotients of Banach-Lie groups thus lead to differing results and the Lie theoretic properties of quotient groups are more accurately described by the Q-group approach than by the approach via topological groups with Lie algebras. 相似文献
12.
We say that is an associative triple in a quasigroup if . It is easy to show that the number of associative triples in Q is at least , and it was conjectured that quasigroups with exactly associative triples do not exist when . We refute this conjecture by proving the existence of quasigroups with exactly associative triples for a wide range of values . Our main tools are quadratic Dickson nearfields and the Weil bound on quadratic character sums. 相似文献
13.
14.
15.
16.
17.
18.
Jimmy Petean 《Journal of Functional Analysis》2019,276(6):1788-1805
Let be any closed Riemannianan manifold and be a Riemannian manifold of constant positive scalar curvature. We prove that the Yamabe equation on the Riemannian product has at least solutions for δ small enough, where denotes the Lusternik–Schnirelmann-category of M. The solutions obtained are functions of M and of them have energy arbitrarily close to the minimum. 相似文献
19.
20.