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The notion of multiple Ore extension is introduced as a natural generalization of Ore extensions and double Ore extensions. For a PBW-deformation of type quantum group, we explicitly obtain the commutation relations of its root vectors, then show that it can be realized via a series of multiple Ore extensions, which we call a ladder Ore extension of type . Moreover, we analyze the quantum algebras with of type , and and give some examples and counterexamples that can be realized by a ladder Ore extension. 相似文献
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Julia Semikina 《Journal of Pure and Applied Algebra》2019,223(10):4509-4523
I. Hambleton, L. Taylor and B. Williams conjectured a general formula in the spirit of H. Lenstra for the decomposition of for any finite group G and noetherian ring R. The conjectured decomposition was shown to hold for some large classes of finite groups. D. Webb and D. Yao discovered that the conjecture failed for the symmetric group , but remarked that it still might be reasonable to expect the HTW-decomposition for solvable groups. In this paper we show that the solvable group is also a counterexample to the conjectured HTW-decomposition. Nevertheless, we prove that for any finite group G the rank of does not exceed the rank of the expression in the HTW-decomposition. We also show that the HTW-decomposition predicts correct torsion for for any finite group G. Furthermore, we prove that for any degree other than the conjecture gives a correct prediction for the rank of . 相似文献
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Let be the finite field of order q. Let G be one of the three groups , or and let W be the standard n-dimensional representation of G. For non-negative integers m and d we let denote the representation of G given by the direct sum of m vectors and d covectors. We exhibit a minimal set of homogeneous invariant polynomials such that for all cases except when and or . 相似文献
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Duc Quang Si 《Journal of Mathematical Analysis and Applications》2021,493(2):124542
Let M be a complete Kähler manifold, whose universal covering is biholomorphic to a ball in (). Our purpose of this article is to establish a non-integrated defect relation with truncated level for a meromorphic mapping on M intersecting a family of hyperplanes in which is non-subdegenerate with respect to the mapping. 相似文献
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Let p be an odd prime number. We describe the Whitehead group of all extra-special and almost extra-special p-groups. For this we compute, for any finite p-group P, the subgroup of , in terms of a genetic basis of P. We also introduce a deflation map , for a normal subgroup N of P, and show that it is always surjective. Along the way, we give a new proof of the result describing the structure of , when P is an elementary abelian p-group. 相似文献
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Francesca Astengo Michael G. Cowling Bianca Di Blasio 《Journal of Functional Analysis》2019,276(1):127-147
We compute the “norm” of irreducible uniformly bounded representations of . We show that the Kunze–Stein version of the uniformly bounded representations has minimal norm in its similarity class of uniformly bounded representations. 相似文献
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Sanming Zhou 《Journal of Pure and Applied Algebra》2019,223(3):931-947
We study two families of cyclotomic graphs and perfect codes in them. They are Cayley graphs on the additive group of , with connection sets and , respectively, where () is an mth primitive root of unity, A a nonzero ideal of , and ? Euler's totient function. We call them the mth cyclotomic graph and the second kind mth cyclotomic graph, and denote them by and , respectively. We give a necessary and sufficient condition for to be a perfect t-code in and a necessary condition for to be such a code in , where is an integer and D an ideal of containing A. In the case when , is known as an Eisenstein–Jacobi and Gaussian networks, respectively, and we obtain necessary conditions for to be a perfect t-code in , where with β dividing α. In the literature such conditions are known to be sufficient when and under an additional condition. We give a classification of all first kind Frobenius circulants of valency 2p and prove that they are all pth cyclotomic graphs, where p is an odd prime. Such graphs belong to a large family of Cayley graphs that are efficient for routing and gossiping. 相似文献
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《Discrete Mathematics》2022,345(1):112640
We show that the lattice point enumerator satisfies for any bounded sets with integer points and all .We also prove that a certain family of compact sets, extending that of cubes , with , minimizes the functional , for any , among those bounded sets with given positive lattice point enumerator.Finally, we show that these new discrete inequalities imply the corresponding classical Brunn-Minkowski and isoperimetric inequalities for non-empty compact sets. 相似文献
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Zhuang He 《Journal of Pure and Applied Algebra》2019,223(10):4426-4445
For every , we find a sufficient condition for the blow-up of a weighted projective space at the identity point not to be a Mori Dream Space. We exhibit several infinite sequences of weights satisfying this condition in all dimensions . 相似文献