Search results for "Incidence algebra"

showing 4 items of 4 documents

Generalised Deformations, Koszul Resolutions, Moyal Products

1998

We generalise Gerstenhaber's theory of deformations, by dropping the assumption that the deformation parameter should commute with the elements of the original algebra. We give the associated cohomology and construct a Koszul resolution for the polynomial algebra [Formula: see text] in the "homogeneous" case. We then develop examples in the case of [Formula: see text] and find some Moyal-like products of a new type. Finally, we show that, for any field K, matrix algebras with coefficients in K and finite degree extensions of K are rigid, as in the commutative case.

AlgebraSymmetric algebraQuadratic algebraQuaternion algebraIncidence algebraSubalgebraDivision algebraAlgebra representationCellular algebraStatistical and Nonlinear PhysicsMathematical PhysicsMathematicsReviews in Mathematical Physics
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Group-graded algebras with polynomial identity

1998

LetG be a finite group and letR=Σg∈GRg be any associative algebra over a field such that the subspacesRg satisfyRgRh⊆Rgh. We prove that ifR1 satisfies a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the order ofG. This result implies the following: ifH is a finite-dimensional semisimple commutative Hopfalgebra andR is anyH-module algebra withRH satisfying a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the dimension ofH.

CombinatoricsFiltered algebraSymmetric algebraIncidence algebraGeneral MathematicsAssociative algebraDivision algebraAlgebra representationCellular algebraComposition algebraMathematics
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An extension of the algebra of sets

1973

We shall explain the aim which leads us in the construction of an extended system of the algebra of sets1. The symbol 1. {*:?(*)} denoting the set of these and only these elements of domain of the variable x which satisfy the propositional condition (propositional function or form) ?9 (x)" is in com? mon use nowadays, so that it is adopted in school courses of mathematics in many countries, and in Poland as well. This condition will be said to define the set 1. However, if we admit propositional conditions which are meaningless for some values of their variables then we encounter some difficulties connected with the ex? pression 1. The formulae 2. {x : 9 (*)} = {x : 9 (*)}' 3. {x : 9 (s) v …

Filtered algebraDiscrete mathematicsHistory and Philosophy of SciencePropositional functionQuaternion algebraLogicIncidence algebraAlgebra of setsTwo-element Boolean algebraNormal extensionField of setsMathematicsStudia Logica
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THE GROUP OF AUTOMORPHISMS OF THE SEMIGROUP OF ENDOMORPHISMS OF FREE COMMUTATIVE AND FREE ASSOCIATIVE ALGEBRAS

2007

Let W(X) be a free commutative or a free associative algebra. The group of automorphisms of the semigroup End (W(X)) is studied.

Symmetric algebraDiscrete mathematicsPure mathematicsIncidence algebraSemigroupGeneral MathematicsFree algebraSubalgebraAssociative algebraFree objectFree probabilityMathematicsInternational Journal of Algebra and Computation
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