共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
3.
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
4.
5.
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
6.
Let be a rational expression of degree three over the finite field . We count the irreducible polynomials in , of a given degree, that have the form for some . As an example of application of our results, we recover the number of irreducible transformation shift registers of order three, which were computed by Jiang and Yang in 2017. 相似文献
7.
8.
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
9.
《Journal of Functional Analysis》2023,284(10):109888
The construction of the free Banach lattice generated by a real Banach space is extended to the complex setting. It is shown that for every complex Banach space E there is a complex Banach lattice containing a linear isometric copy of E and satisfying the following universal property: for every complex Banach lattice , every operator admits a unique lattice homomorphic extension with . The free complex Banach lattice is shown to have analogous properties to those of its real counterpart. However, examples of non-isomorphic complex Banach spaces E and F can be given so that and are lattice isometric. The spectral theory of induced lattice homomorphisms on is also explored. 相似文献
10.
11.
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
12.
13.
14.
16.
17.
18.
20.