Results 251 to 260 of about 761,977 (284)

Symmetric identities in graded algebras

Archiv der Mathematik, 1997
The interest in the symmetric polynomial identity \[ P_n(x_1,\ldots,x_n)=\sum_{\sigma\in S_n}x_{\sigma(1)}\ldots x_{\sigma(n)} \] in the theory of PI-algebras originates from the fact that over a field of characteristic 0 this identity is equivalent to the nil identity and the Nagata-Higman theorem gives that the algebra is nilpotent. The recent result
Bahturin, Y. A., Giambruno, A., Zaicev, M. V.   +2 more
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Two Symmetric Identities Involving Complete and Elementary Symmetric Functions

Bulletin of the Malaysian Mathematical Sciences Society, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On algebras satisfying symmetric identities

Archiv der Mathematik, 1994
Consider the non-commutative polynomials \[ s_ n = \sum_{\pi \in \text{Sym}(n)} x_{\pi(1)} \dots x_{\pi(n)}\quad \text{and} \quad d_ n = \sum_{\pi \in \text{Sym}(n)} x_{\pi(1)} y_ 1 \dots y_{n - 1} x_{\pi(n)}. \] Let \(R\) be an algebra over a field of characteristic \(p > 0\). We show that if \(s_ n = 0\) (\(d_ n = 0\), resp.) is a polynomial identity
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Identity-Based Symmetric Private Set Intersection

2013 International Conference on Social Computing, 2013
A private set intersection (PSI) protocol enables two parties to privately compute the intersection of their inputs. Most of its previous versions are unilateral, that is, only one party can learn the intersection and the other learns nothing. Many applications require that both parties can obtain the final result.
Shuo Qiu, Jiqiang Liu, Yanfeng Shi
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Representationalism, Symmetrical Supervenience and Identity

Philosophia, 2008
According to some representationalists (M. Tye, Ten problems of consciousness, MIT Press, Massachusetts, USA, 1995; W.G. Lycan, Consciousness and experience, MIT Press, Cambridge, Massachusetts, USA, 1996; F. Dretske, Naturalising the mind, MIT Press, Massachusetts, USA 1995), qualia are identical to external environmental states or features.
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COMMUTATOR IDENTITIES ON SYMMETRIC ELEMENTS OF GROUP ALGEBRAS

Journal of Algebra and Its Applications, 2013
Let K be a field of odd characteristic p, and let G be the direct product of a finite p-group P ≠ 1 and a Hamiltonian 2-group. We show that the set of symmetric elements (KG)* of the group algebra KG with respect to the involution of KG which inverts all elements of G, satisfies all Lie commutator identities of degree t(P) or more, where t(P) denotes ...
Juhász, Tibor, Tóth, Enikő
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Group Identities on Symmetric Units

2010
Let F be an infinite field of characteristic different from 2 and G a group. We examine the set of units, \({\mathcal{U}}^{+}(FG)\), symmetric under the natural involution ∗ sending each group element to its inverse. The conditions under which \({\mathcal{U}}^{+}(FG)\) satisfies a group identity are presented, subject to the restriction that G ∕ T is a
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Identities and Inequalities via Symmetrization

1983
The purpose of this survey paper is to examine some specific applications of the process of averaging over finite groups, compact topological groups, and compact homogeneous manifolds. These applications occur in a variety of different disciplines of pure and applied mathematics, such as (i) classical representation theory of finite groups, (ii ...
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On Permanental Identities of Symmetric and Skew-Symmetric Matrices in Characteristic p

Canadian Mathematical Bulletin, 1998
AbstractLet Mn(F) be the algebra of n × n matrices over a field F of characteristic p > 2 and let * be an involution on Mn(F). If s1,…,sr are symmetric variables we determine the smallest r such that the polynomialis a *-polynomial identity of Mn(F) under either the symplectic or the transpose involution.
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ANTI-COMMUTATIVE ALGEBRAS WITH SKEW-SYMMETRIC IDENTITIES

Journal of Algebra and Its Applications, 2009
Generalizing Lie algebras, we consider anti-commutative algebras with skew-symmetric identities of degree > 3. Given a skew-symmetric polynomial f, we call an anti-commutative algebra f-Lie if it satisfies the identity f = 0. If sn is a standard skew-symmetric polynomial of degree n, then any s4-Lie algebra is f-Lie if deg f ≥ 4. We describe a free
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