Cohomology and group extensions in Magma

Discovering Mathematics with Magma - Algorithms and Computation in Mathematics ◽

10.1007/978-3-540-37634-7_10 ◽

2007 ◽

pp. 221-241 ◽

Cited By ~ 2

Author(s):

Derek F. Holt

Keyword(s):

Group Extensions

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Finite group extensions of irrational rotations

Israel Journal of Mathematics ◽

10.1007/bf02760801 ◽

1975 ◽

Vol 21 (2-3) ◽

pp. 240-259 ◽

Cited By ~ 11

Author(s):

William A. Veech

Keyword(s):

Finite Group ◽

Irrational Rotations ◽

Group Extensions

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PBW deformations of quantum symmetric algebras and their group extensions

Journal of Algebra and Its Applications ◽

10.1142/s0219498816500493 ◽

2016 ◽

Vol 15 (03) ◽

pp. 1650049 ◽

Cited By ~ 2

Author(s):

Piyush Shroff ◽

Sarah Witherspoon

Keyword(s):

Finite Group ◽

Lie Algebra ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Group Extensions ◽

Enveloping Algebra ◽

Symmetric Algebras ◽

Necessary And Sufficient ◽

Special Case

We examine PBW deformations of finite group extensions of quantum symmetric algebras, in particular the quantum Drinfeld orbifold algebras defined by the first author. We give a homological interpretation, in terms of Gerstenhaber brackets, of the necessary and sufficient conditions on parameter functions to define a quantum Drinfeld orbifold algebra, thus clarifying the conditions. In case the acting group is trivial, we determine conditions under which such a PBW deformation is a generalized enveloping algebra of a color Lie algebra; our PBW deformations include these algebras as a special case.

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A note on central group extensions

Journal of the Australian Mathematical Society ◽

10.1017/s1446788700028780 ◽

1973 ◽

Vol 15 (4) ◽

pp. 428-429 ◽

Cited By ~ 1

Author(s):

G. J. Hauptfleisch

Keyword(s):

Abelian Group ◽

Homomorphic Image ◽

Free Group ◽

Central Extension ◽

Dihedral Group ◽

Group Extension ◽

Central Group ◽

Group Extensions

If A, B, H, K are abelian group and φ: A → H and ψ: B → K are epimorphisms, then a given central group extension G of H by K is not necessarily a homomorphic image of a group extension of A by B. Take for instance A = Z(2), B = Z ⊕ Z, H = Z(2), K = V4 (Klein's fourgroup). Then the dihedral group D8 is a central extension of H by K but it is not a homomorphic image of Z ⊕ Z ⊕ Z(2), the only group extension of A by the free group B.

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