Search results for "Cellular algebra"

showing 6 items of 16 documents

The Representation Type of the Centre of a Group Algebra

1986

Filtered algebraSymmetric algebraAlgebraPure mathematicsGeneral MathematicsAlgebra representationCellular algebraRepresentation theory of Hopf algebrasUniversal enveloping algebraGroup algebraMathematicsGroup ringJournal of the London Mathematical Society

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On the Directly and Subdirectly Irreducible Many-Sorted Algebras

2015

AbstractA theorem of single-sorted universal algebra asserts that every finite algebra can be represented as a product of a finite family of finite directly irreducible algebras. In this article, we show that the many-sorted counterpart of the above theorem is also true, but under the condition of requiring, in the definition of directly reducible many-sorted algebra, that the supports of the factors should be included in the support of the many-sorted algebra. Moreover, we show that the theorem of Birkhoff, according to which every single-sorted algebra is isomorphic to a subdirect product of subdirectly irreducible algebras, is also true in the field of many-sorted algebras.

Pure mathematicslcsh:MathematicsGeneral MathematicsSubalgebraUniversal enveloping algebralcsh:QA1-939directly irreducible many-sorted algebraSubdirect productsymbols.namesakemany-sorted algebraSubdirectly irreducible algebraAlgebra representationsymbolsDivision algebraMathematics::Metric GeometryCellular algebrasupport of a many-sorted algebrasubdirectly irreducible many-sorted algebraMathematicsFrobenius theorem (real division algebras)Demonstratio Mathematica

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An Operator Theoretical Approach to Enveloping ϕ* - and C* - Algebras of Melrose Algebras of Totally Characteristic Pseudodifferential Operators

1998

Let X be a compact manifold with boundary. It will be shown (Theorem 3.4) that the small Melrose algebra A≔ ϕb,cl (χ,bΩ1/2) (cf. [22], [23]) of classical, totally characteristic pseudodifferential operators carries no topology such that it is a topological algebra with an open group of invertible elements, in particular, the algebra A cannot be spectrally invariant in any C* – algebra. On the other hand, the symbolic structure of A can be extended continuously to the C* – algebra B generated by A as a subalgebra of ζ(σbL2(χ, bΩ1/2)) by a generalization of a method of Gohberg and Krupnik. Furthermore, A is densely embedded in a Frechet algebra A ⊆ B which is a ϕ* – algebra in the sense of Gr…

Symmetric algebraDiscrete mathematicsFiltered algebraPure mathematicsGeneral MathematicsDifferential graded algebraSubalgebraAlgebra representationDivision algebraCellular algebraUniversal enveloping algebraMathematicsMathematische Nachrichten

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On the projectives of a group algebra

1980

Symmetric algebraFiltered algebraPure mathematicsGeneral MathematicsDifferential graded algebraDivision algebraCellular algebraUniversal enveloping algebraGroup algebraCentral simple algebraMathematicsMathematische Zeitschrift

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Hom-Lie quadratic and Pinczon Algebras

2017

ABSTRACTPresenting the structure equation of a hom-Lie algebra 𝔤, as the vanishing of the self commutator of a coderivation of some associative comultiplication, we define up to homotopy hom-Lie algebras, which yields the general hom-Lie algebra cohomology with value in a module. If the hom-Lie algebra is quadratic, using the Pinczon bracket on skew symmetric multilinear forms on 𝔤, we express this theory in the space of forms. If the hom-Lie algebra is symmetric, it is possible to associate to each module a quadratic hom-Lie algebra and describe the cohomology with value in the module.