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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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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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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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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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Let q be a perfect power of a prime number p and be an elliptic curve over given by the equation . For a positive integer n we denote by the number of rational points on E (including infinity) over the extension . Under a mild technical condition, we show that the sequence contains at most 10200 perfect squares. If the mild condition is not satisfied, then is a perfect square for infinitely many n including all the multiples of 12. Our proof uses a quantitative version of the Subspace Theorem. We also find all the perfect squares for all such sequences in the range and . 相似文献
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We give an improvement on a character sum estimate in and answer a question of Shparlinski. 相似文献
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Let be the finite field with q elements, and T a positive integer. In this article, we find an asymptotic formula for the total number of monic irreducible binomials in of degree less or equal to T, when T is large enough. We also show explicit lower and upper bounds for the number of binomials in the case when T is small. 相似文献
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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
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《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
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