A construction of generalized Jacobian varieties by group extensions

1962 ◽  
Vol 147 (4) ◽  
pp. 277-286 ◽  
Author(s):  
F. Oort
Keyword(s):  
Generalized Jacobian ◽  
Group Extensions ◽  
Jacobian Varieties

Generalized Jacobian Varieties

1954 ◽  
Vol 59 (3) ◽  
pp. 505 ◽  
Author(s):  
Maxwell Rosenlicht
Keyword(s):  
Generalized Jacobian ◽  
Jacobian Varieties

scholarly journals On real generalized Jacobian varieties

2005 ◽  
Vol 203 (1-3) ◽  
pp. 252-274 ◽  
Author(s):  
Jean-Philippe Monnier
Keyword(s):  
Generalized Jacobian ◽  
Jacobian Varieties

scholarly journals Generalized Jacobian Varieties and Separable Abelian Extensions of Function Fields

1957 ◽  
Vol 12 ◽  
pp. 231-254 ◽  
Author(s):  
Hisasi Morikawa
Keyword(s):  
Field Theory ◽  
Finite Fields ◽  
Function Fields ◽  
Abelian Extension ◽  
Jacobian Variety ◽  
Generalized Jacobian ◽  
Abelian Extensions ◽  
Jacobian Varieties ◽  
Several Variables ◽  
Class Fields

Using Frobenius automorphisms ingeniouslly, S. Lang has established an elegant theory of unramified class fields of function fields in several variables over finite fields [2]. As an application of class field theory and theory of reduction he has proved that any separable unramified abelian extension of a function field of one variable comes from a pull back of a separable ingeny of its jacobian variety [3].

PBW deformations of quantum symmetric algebras and their group extensions

2016 ◽  
Vol 15 (03) ◽  
pp. 1650049 ◽  
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.

scholarly journals A note on central group extensions

1973 ◽  
Vol 15 (4) ◽  
pp. 428-429 ◽  
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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