共查询到20条相似文献,搜索用时 31 毫秒
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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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We construct invariant polynomials on truncated multicurrent algebras, which are Lie algebras of the form , where is a finite-dimensional Lie algebra over a field of characteristic zero, and I is a finite-codimensional ideal of generated by monomials. In particular, when is semisimple and is algebraically closed, we construct a set of algebraically independent generators for the algebra of invariant polynomials. In addition, we describe a transversal slice to the space of regular orbits in . As an application of our main result, we show that the center of the universal enveloping algebra of acts trivially on all irreducible finite-dimensional representations provided I has codimension at least two. 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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L. Emily Cowie Hans-Christian Herbig Daniel Herden Christopher Seaton 《Journal of Pure and Applied Algebra》2019,223(1):395-421
Let V be a finite-dimensional representation of the complex circle determined by a weight vector . We study the Hilbert series of the graded algebra of polynomial -invariants in terms of the weight vector a of the -action. In particular, we give explicit formulas for as well as the first four coefficients of the Laurent expansion of at . The naive formulas for these coefficients have removable singularities when weights pairwise coincide. Identifying these cancelations, the Laurent coefficients are expressed using partial Schur polynomials that are independently symmetric in two sets of variables. We similarly give an explicit formula for the a-invariant of in the case that this algebra is Gorenstein. As an application, we give methods to identify weight vectors with Gorenstein and non-Gorenstein invariant algebras. 相似文献
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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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Tadahiro Miyao 《Journal of Functional Analysis》2019,276(6):1948-1977
We consider the renormalized Nelson model at a fixed total momentum P: ; the Hamiltonian is defined through an infinite energy renormalization. We prove that is positivity improving for all and in the Fock representation. 相似文献