共查询到20条相似文献，搜索用时 0 毫秒
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Oliver Villa 《代数通讯》2017,45(5):2047-2051
We study the conjugacy classes of elements of a finite-dimensional central simple associative algebra with respect to scalar extensions. We apply the results to investigate the products of two (skew-)symmetric elements in central simple algebras with involution. 相似文献
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《代数通讯》2013,41(4):965-986
ABSTRACT An exact sequence of Witt groups, motivated by exact sequences obtained by Lewis and by Parimala, Sridharan and Suresh, is constructed. The behavior of the maps involved in these sequences with respect to isotropy is completely determined in the case of division algebras. In particular, the kernels of the maps involved in the previous sequences are explicitly given, leading to a new proof of their exactness. Similar exact sequences of equivariant Witt groups are constructed. As an application, relations between the cardinality of certain Witt groups are obtained. 相似文献
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J. Z. Gonçalves 《代数通讯》2013,41(8):3113-3121
Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a b } freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality |k| (which need not be open). 相似文献
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Demba Barry 《代数通讯》2013,41(9):3767-3787
Let A be a central simple algebra over a field F. Let k1,…, kr be cyclic extensions of F such that k1 ?F… ?Fkr is a field. We investigate conditions under which A is a tensor product of symbol algebras where each field ki lies in a symbol F-algebra factor of the same degree as ki over F. As an application, we give an example of an indecomposable algebra of degree 8 and exponent 2 over a field of 2-cohomological dimension 4. 相似文献
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A.-H. Nokhodkar 《代数通讯》2017,45(3):1019-1027
We investigate the Wall form of unipotent elements of index two in the orthogonal group and obtain a decomposition for these elements. Also, in characteristic two, the relation between the Wall form and some invariants of the induced involution on the Clifford algebra is studied. 相似文献
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M. Chacron 《代数通讯》2013,41(9):3951-3965
We are given a semiprime unital ring A with * such that x*x = xx* for all elements x of A. We will show that both elements x + x* and xx* are central elements. In the case in which A is a quaternion algebra over a field F in the sense given by Albert, we show that * is unique and coincides with the canonical involution. We also provide specific constructions of quaternion division algebras A with canonical involution over a field F of one of the following types: (i) F is a function field in two variables over a ground field of unspecified characteristic; (ii) F is a function field over the Galois field GF(2n); and (iii) F is a function field over the Galois field GF(pn) where p is an odd prime number and n is a natural number. 相似文献
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M. R. Omar 《代数通讯》2013,41(4):1351-1362
We compute the Lie algebra of a higher degree hyperbolic alternating form, which generalizes the symplectic algebra to higher degrees. We use this to show that hyperbolic forms descend under scalar extension. An immediate consequence is that a version of the weak Hasse–Minkowski Theorem is valid for alternating forms of higher degree. 相似文献
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We define a notion of Morita equivalence between algebras with antiautomorphisms such that two equivalent algebras have the same category of sesquilinear forms. This generalizes the Morita equivalence of algebras with involutions defined by Fröhlich and Mc Evett [5], and their categories of ?-hermitian forms. For two Morita equivalent algebras with involution, with an additional technical property (which is true for central simple algebras), we define a new algebra with antiautomorphism, called the orthogonal sum, which generalizes the usual notion of orthogonal sum of forms. We explore the invariants of this sum. 相似文献
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We will complete the list of universal binary Hermitian forms over imaginary quadratic fields by investigating three Hermitian forms missed by previous researchers.
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Simple algebras of Weyl type 总被引：9，自引：0，他引：9
Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A⊗F[D] from any pair of a commutative associative algebra,A with an identity element and the polynomial algebraF[D] of a commutative derivation subalgebraD ofA We prove thatA[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only ifA isD-simple andA[D] acts faithfully onA. Thus we obtain a lot of simple algebras.
Su, Y., Zhao, K., Second cohornology group of generalized Witt type Lie algebras and certain representations, submitted to
publication 相似文献
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David J. Winter 《代数通讯》2013,41(4):1093-1126
A Lie algop is a pair (A, L) where A is a commutative algebra and L is a Lie algebra operating on A by derivations. Faithful simple Lie algops (A, L) are of interest because the corresponding Lie algebras AL are simple—with some rare exceptions at characteristic 2. The simplicity and representation theory of Jordan Lie algops is reduced in Winter (2005b) to the simplicity theory of nil Lie algops and the simplicity and representation theory of toral Lie algops. This paper is devoted to building the first of these two theories, the simplicity theory of nil Lie algops, as a structure theory. 相似文献
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Denis SERRE 《数学年刊B辑(英文版)》2009,30(6):785-802
The roots of hyperbolic polynomials satisfy the linear inequalities that were previously established for the eigenvalues of Hermitian matrices, after a conjecture by A. Horn. Among them are the so-called Weyl and Lidskiǐ inequalities. An elementary proof of the latter for hyperbolic polynomials is given. This proof follows an idea from H. Weinberger and is free from representation theory and Schubert calculus arguments, as well as from hyperbolic partial differential equations theory. 相似文献
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A.-H. Nokhodkar 《代数通讯》2013,41(12):5283-5289
ABSTRACTSome necessary and su?cient conditions are obtained for a totally decomposable algebra with orthogonal involution in characteristic two to have a separable descent. 相似文献
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Denis SERRE 《数学年刊B辑(英文版)》2009,30(6)
The roots of hyperbolic polynomials satisfy the linear inequalities that were previously established for the eigenvalues of Hermitian matrices, after a conjecture by A. Horn. Among them are the so-called Weyl and Lidski(i) inequalities. An elementary proof of the latter for hyperbolic polynomials is given. This proof follows an idea from H. Weinberger and is free from representation theory and Schubert calculus arguments, as well as from hyperbolic partial differential equations theory. 相似文献
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设D 是带对合的除环. 当char(D) ≠ 2 时, D 上Hermitian 矩阵几何的基本定理最近已经证明.作者进一步证明了特征2 的带对合的除环上Hermitian 矩阵几何的基本定理, 从而得到任意带对合的除环上Hermitian 矩阵几何的基本定理. 相似文献
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Positivity in *-algebras can be defined either algebraically, by quadratic modules, or analytically, by *-representations. By the induction procedure for *-representations, we can lift the analytical notion of positivity from a *-subalgebra to the entire *-algebra. The aim in this article is to define and study the induction procedure for quadratic modules. The main question is when a given quadratic module on the *-algebra is induced from its intersection with the *-subalgebra. This question is very hard even for the smallest quadratic module (i.e. the set of all sums of hermitian squares) and will be answered only in very special cases. 相似文献
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Chi-Kwong Li Ilya M. Spitkovsky 《Journal of Mathematical Analysis and Applications》2003,282(1):329-340
Existence of the fractional powers is established in Banach algebra setting, in terms of the numerical ranges of elements involved. The behavior of the spectra and (for Hermitian ∗-algebras satisfying some additional hypotheses) the ∗-numerical range under taking these powers also is investigated. 相似文献