Search results for "Covering group"

showing 5 items of 5 documents

Some results concerning simple locally finite groups of 1-type

2005

AbstractIn this paper several aspects of infinite simple locally finite groups of 1-type are considered. In the first part, the classes of diagonal limits of finite alternating groups, of diagonal limits of finite direct products of alternating groups, and of absolutely simple groups of 1-type are distinguished from each other. In the second part, inductive systems of representations over fields of characteristic zero (which are known to correspond to ideals in the group algebra) are studied in general for groups of 1-type. The roles of primitive respectively imprimitive representations in inductive systems are investigated. Moreover it is shown that in any proper inductive system the depth…

Discrete mathematicsAlgebra and Number TheoryProfinite groupGroup ringsGroup (mathematics)Inductive systemsSimple groupsCovering groups of the alternating and symmetric groupsLocally finite groupsGroup of Lie typeSymmetric groupSimple groupClassification of finite simple groupsGroup theoryMathematicsJournal of Algebra
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Central idempotents and units in rational group algebras of alternating groups

1998

Let ℚAn be the group algebra of the alternating group over the rationals. By exploiting the theory of Young tableaux, we give an explicit description of the minimal central idempotents of ℚAn. As an application we construct finitely many generators for a subgroup of finite index in the centre of the group of units of ℚAn.

CombinatoricsRational numberSymmetric groupGeneral MathematicsRational groupGenerating set of a groupYoung tableauAlternating groupGroup algebraCovering groups of the alternating and symmetric groupsMathematics
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On permutations of class sums of alternating groups

1997

We prove a result concerning the class sums of the alternating group An; as a consequence we deduce that if θ is a normalized automorphism of the integral group ring then there exists such that is the identity on , where Sn:is the symmetric group and is the center of

Combinatoricsp-groupAlgebra and Number TheoryInner automorphismSymmetric groupOuter automorphism groupAlternating groupPermutation groupDihedral group of order 6Covering groups of the alternating and symmetric groupsMathematicsCommunications in Algebra
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Invariant ordering of surface groups and 3-manifolds which fibre over $S^1$

2006

CombinatoricsDicyclic groupGeneral MathematicsInvariant (mathematics)Point groups in two dimensionsCovering groups of the alternating and symmetric groupsMathematicsNon-abelian groupMathematical Proceedings of the Cambridge Philosophical Society
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Star representations of E(2)

1990

We give a complete and explicit realization of the unitary irreducible representations of the universal covering group G of E(2), the Euclidean group in two dimensions, by deformation of the algebra of functions on the dual g* of the Lie algebra of G. We define an adapted Fourier transform for G which gives a natural description of the harmonic analysis of G.

AlgebraUnitary representationRepresentation theory of SURepresentation theory of the Lorentz groupCovering groupZonal spherical functionStatistical and Nonlinear PhysicsUniversal enveloping algebra(gK)-moduleGroup algebraMathematical PhysicsMathematicsLetters in Mathematical Physics
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