Search results for "rete"

showing 10 items of 3470 documents

Einklassige Geschlechter totalpositiver quadratischer Formen in totalreellen algebraischen Zahlkörpern

1971

Abstract It is proved that totally positive quadratic forms with three or more variables and class number h = 1 exist only in a finite number of algebraic number fields. Each field allows only a finite number of such forms with bounded scale. To prove this, upper estimates for all local factors in Siegel's analytic formula are constructed by calculating explicitly numbers of solutions of quadratic congruences.

Discrete mathematicsPure mathematicsAlgebra and Number TheoryQuadratic equationBounded functionBinary quadratic formField (mathematics)Quadratic fieldAlgebraic numberCongruence relationFinite setMathematicsJournal of Number Theory
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Lie nilpotence of group rings

1993

Let FG be the group algebra of a group G over a field F. Denote by ∗ the natural involution, (∑fi gi -1. Let S and K denote the set of symmetric and skew symmetric and skew symmetric elements respectively with respect to this involutin. It is proved that if the characteristic of F is zero p≠2 and G has no 2-elements, then the Lie nilpotence of S or K implies the Lie nilpotence of FG.

Discrete mathematicsPure mathematicsAlgebra and Number TheoryRepresentation of a Lie groupTriple systemSimple Lie groupAdjoint representationSkew-symmetric matrixWeightGroup algebraGroup ringMathematicsCommunications in Algebra
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A restriction on the schur multiplier of nilpotent lie algebras

2011

An improvement of a bound of Yankosky (2003) is presented in this paper, thanks to a restriction which has been recently obtained by the authors on the Schur multiplier M(L) of a finite dimensional nilpotent Lie algebra L. It is also described the structure of all nilpotent Lie algebras such that the bound is attained. An important role is played by the presence of a derived subalgebra of maximal dimension. This allows precision on the size of M(L). Among other results, applications to the non-abelian tensor square L ⊗ L are illustrated.

Discrete mathematicsPure mathematicsAlgebra and Number TheorySchur multiplierSchur's lemmanilpotent Lie algebrasSchur algebrahomology of Lie algebraSchur's theoremLie conformal algebraNilpotent Lie algebraSettore MAT/02 - AlgebraAdjoint representation of a Lie algebraRepresentation of a Lie groupNilpotent groupMathematics::Representation TheoryMathematics
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Group algebras and Lie nilpotence

2013

Abstract Let ⁎ be an involution of a group algebra FG induced by an involution of the group G. For char F ≠ 2 , we classify the groups G with no 2-elements and with no nonabelian dihedral groups involved whose Lie algebra of ⁎-skew elements is nilpotent.

Discrete mathematicsPure mathematicsAlgebra and Number TheorySimple Lie group010102 general mathematicsMathematics::Rings and AlgebrasUniversal enveloping algebra0102 computer and information sciencesGroup algebraSkew-symmetric element01 natural sciencesRepresentation theoryLie conformal algebraGraded Lie algebraRepresentation of a Lie groupgroup algebra unit010201 computation theory & mathematicsLie nilpotentGroup algebra0101 mathematicsNilpotent groupANÉIS E ÁLGEBRAS ASSOCIATIVOSMathematicsJournal of Algebra
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Group algebras of torsion groups and Lie nilpotence

2010

Letbe an involution of a group algebra FG induced by an involution of the group G. For char F 0 2, we classify the torsion groups G with no elements of order 2 whose Lie al- gebra of � -skew elements is nilpotent.

Discrete mathematicsPure mathematicsAlgebra and Number TheorySimple Lie groupAdjoint representationANÉIS DE GRUPOSGroup algebraRepresentation theoryGraded Lie algebraNon-abelian groupRepresentation of a Lie groupgroup algebra unitNilpotent groupMathematicsJournal of Group Theory
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Irreducible Finitary Lie Algebras over Fields of Characteristic Zero

1998

Abstract A Lie subalgebraLof g l K (V) is said to befinitaryif it consists of elements of finite rank. We show that if Char  K  = 0, if dim K  Vis infinite, and ifLacts irreducibly onV, then the derived algebra ofLis simple.

Discrete mathematicsPure mathematicsAlgebra and Number TheorySimple Lie groupNon-associative algebraFundamental representation(gK)-moduleKilling formAffine Lie algebraMathematicsLie conformal algebraGraded Lie algebraJournal of Algebra
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Polynomial codimension growth of algebras with involutions and superinvolutions

2017

Abstract Let A be an associative algebra over a field F of characteristic zero endowed with a graded involution or a superinvolution ⁎ and let c n ⁎ ( A ) be its sequence of ⁎-codimensions. In [4] , [12] it was proved that if A is finite dimensional such sequence is polynomially bounded if and only if A generates a variety not containing a finite number of ⁎-algebras: the group algebra of Z 2 and a 4-dimensional subalgebra of the 4 × 4 upper triangular matrices with suitable graded involutions or superinvolutions. In this paper we focus our attention on such algebras since they are the only finite dimensional ⁎-algebras, up to T 2 ⁎ -equivalence, generating varieties of almost polynomial gr…

Discrete mathematicsPure mathematicsAlgebra and Number TheorySubvarietySuperinvolution010102 general mathematicsSubalgebraGraded involution; Growth; Polynomial identity; SuperinvolutionTriangular matrix010103 numerical & computational mathematicsGroup algebraCodimensionPolynomial identity Graded involution Superinvolution GrowthGrowthPolynomial identity01 natural sciencesGraded involutionSettore MAT/02 - AlgebraBounded functionAssociative algebra0101 mathematicsFinite setMathematics
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Preduals of spaces of homogeneous polynomials onLp-spaces

2012

Given a regular probability measure μ on a compact Hausdorff space, we explicitly describe the predual of the Banach space of continuous n-homogeneous polynomials on L p (μ) as the completion of a (explicit constructed) subspace of L p/n (μ) with respect to a (explicitly constructed) norm π p/n . An application to the factorization of dominated polynomials is provided.

Discrete mathematicsPure mathematicsAlgebra and Number TheoryTopological tensor productHausdorff spaceBanach spaceInterpolation spacePredualBirnbaum–Orlicz spaceBanach manifoldLp spaceMathematicsLinear and Multilinear Algebra
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Fixed point theorems for non-self mappings in symmetric spaces under φ-weak contractive conditions and an application to functional equations in dyna…

2014

In this paper, we prove some common fixed point theorems for two pairs of non-self weakly compatible mappings enjoying common limit range property, besides satisfying a generalized phi-weak contractive condition in symmetric spaces. We furnish some illustrative examples to highlight the realized improvements in our results over the corresponding relevant results of the existing literature. We extend our main result to four finite families of mappings in symmetric spaces using the notion of pairwise commuting mappings. Finally, we utilize our results to discuss the existence and uniqueness of solutions of certain system of functional equations arising in dynamic programming.

Discrete mathematicsPure mathematicsApplied Mathematics010102 general mathematicsFixed-point theoremcommon fixed pointweakly compatible mappingSymmetric space01 natural sciences010101 applied mathematicsDynamic programmingComputational MathematicsRange (mathematics)Settore MAT/05 - Analisi MatematicaSymmetric spacePairwise comparisonLimit (mathematics)Uniqueness0101 mathematicscommon limit range propertyCoincidence pointMathematicsApplied Mathematics and Computation
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Lp-Spaces as Quasi *-Algebras

1996

Abstract The Banach space L p ( X , μ), for X a compact Hausdorff measure space, is considered as a special kind of quasi *-algebra (called CQ*-algebra) over the C*-algebra C ( X ) of continuous functions on X . It is shown that, for p ≥2, ( L p ( X , μ),  C ( X )) is *-semisimple (in a generalized sense). Some consequences of this fact are derived.

Discrete mathematicsPure mathematicsApplied MathematicsBanach spaceHausdorff spaceAnalysiSpace (mathematics)C*-algebraCompact spaceOperator algebraHausdorff measureLp spaceSettore MAT/07 - Fisica MatematicaAnalysisMathematicsJournal of Mathematical Analysis and Applications
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