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We present some fundamental results on (possibly nonlinear) algebraic semigroups and monoids. These include a version of Chevalley's structure theorem for irreducible algebraic monoids, and the description of all algebraic semigro...
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We present some fundamental results on (possibly nonlinear) algebraic semigroups and monoids. These include a version of Chevalley's structure theorem for irreducible algebraic monoids, and the description of all algebraic semigroup structures on curves and complete varieties.
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In this paper, we show the characterization theorem of lattice implication algebras. The algebras were presented by Xu (J. Southwest Jiaotong Univ., p.20-27) in 1993. Our theorem means that the class of all lattice implication alg...
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In this paper, we show the characterization theorem of lattice implication algebras. The algebras were presented by Xu (J. Southwest Jiaotong Univ., p.20-27) in 1993. Our theorem means that the class of all lattice implication algebras coincides with the class of all bounded commutative BCK-algebras. Hence lattice implication algebras are categorically equivalent to MV-algebras and to Wajsberg algebras.
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摘要 :
In this paper, we show the characterization theorem of lattice implication algebras. The algebras were presented by Xu (J. Southwest Jiaotong Univ., p.20-27) in 1993. Our theorem means that the class of all lattice implication alg...
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In this paper, we show the characterization theorem of lattice implication algebras. The algebras were presented by Xu (J. Southwest Jiaotong Univ., p.20-27) in 1993. Our theorem means that the class of all lattice implication algebras coincides with the class of all bounded commutative BCK-algebras. Hence lattice implication algebras are categorically equivalent to MV-algebras and to Wajsberg algebras.
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We give functorial recipes to get, out of any Hopf algebra over a field, two pairs of Hopf algebras bearing some geometrical content. If the ground field has zero characteristic, the first pair is made of a function algebra F[G_|_...
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We give functorial recipes to get, out of any Hopf algebra over a field, two pairs of Hopf algebras bearing some geometrical content. If the ground field has zero characteristic, the first pair is made of a function algebra F[G_|_] over a connected Poiason group and a universal enveloping algebra U(g-) over a Lie bialgebra Q- : in addition, the Poisson group as a variety is an afflne space, and the Lie bialgebra aa a Lie algebra is graded; apart for these last details, the second pair is of the same type, namely (.F[G_], [f(g+)) for some Poisson group G_ and some Lie bialgebra g+. When the Hopf algebra H we start from is already of geometric type the result involves Poisson duality: the first Lie bialgebra associated to if = F[G] is g* (with g := Lie(G)), and the first Poisson group associated to H = U(g) is of type G*, i.e. it has g as cotangent Lie bialgebra. If the ground field has positive characteristic, then the same recipes give similar results, but for the fact that the Poisson groups obtained have dimension 0 and height 1, and restricted universal enveloping algebras are obtained. We show how all these "geometrical" Hopf algebras are linked to the original one via 1-parameter deformations, and explain how these results follow from quantum group theory.
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Let Ω be an arbitrary family of non-isomorphic n-dimensional alternative algebras over algebraically closed field k that depends continuously on a certain set of parameters p_1,...,p_N. Then the asymptotic of the dimension of Ω,...
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Let Ω be an arbitrary family of non-isomorphic n-dimensional alternative algebras over algebraically closed field k that depends continuously on a certain set of parameters p_1,...,p_N. Then the asymptotic of the dimension of Ω, that is the largest possible number N of parameters, is4/27n~3+ O(n~(8/3)). We also formulate a conjecture for the asymptotic of the 7 number of parameters to define irreducible family of n-dimensional Jordan algebras, namely N =1/6 (3)~(1/2) +0(n~(8/3)). We prove it for some closed subvariety of the variety of Jordan algebras.
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In this chapter we present a decomposition of the subalgebra T(G) of Hom(A(G)) generated by {id.4(GI} U {Lt\L,: A(G) -?A(G), t ? A(G)}, where G is a graph, A(G) is the Bernstein graph algebra of G, id.,^., is the identity function...
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In this chapter we present a decomposition of the subalgebra T(G) of Hom(A(G)) generated by {id.4(GI} U {Lt\L,: A(G) -?A(G), t ? A(G)}, where G is a graph, A(G) is the Bernstein graph algebra of G, id.,^., is the identity function on A(G) and Lt is the left (= right) multiplication by t. If G is a simple connected graph, without loop and |V(Cr)| > 2, then we present a characterization of T(G).
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This is a survey paper on classification problems of some classes of algebras introduced by Loday around 1990s. In the paper the author intends to review the latest results on classification problem of Loday algebras, achievements...
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This is a survey paper on classification problems of some classes of algebras introduced by Loday around 1990s. In the paper the author intends to review the latest results on classification problem of Loday algebras, achievements have been made up to date, approaches and methods implemented.
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The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP 2005].
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In this paper we consider Arens and Tracial algebras which were introduced in [8, 9]. We also investigate their algebraical and topological properties, and study relations between Arens algebras, Tracial algebras and underlying vo...
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In this paper we consider Arens and Tracial algebras which were introduced in [8, 9]. We also investigate their algebraical and topological properties, and study relations between Arens algebras, Tracial algebras and underlying von Neumann algebra.
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On any set X may be defined the free algebra R〈X〉* (respectively, free commutative algebra R[X]) with coefficients in a ring R. It may also be equivalently described as the algebra of the free monoid X* (respectively, free commu...
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On any set X may be defined the free algebra R〈X〉* (respectively, free commutative algebra R[X]) with coefficients in a ring R. It may also be equivalently described as the algebra of the free monoid X* (respectively, free commutative monoid M(X)). Furthermore, the algebra of differential polynomials R{X} with variables in X may be constructed. The main objective of this contribution is to provide a functorial description of this kind of objects with their relations (including abelianization and unitarization) in the category of differential algebras, and also to introduce new structures such as the differential algebra of a semigroup, of a monoid, or the universal differential envelope of an algebra.
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