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  • Electronic Resource  (2)
  • 81S99  (2)
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  • Electronic Resource  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    Universal deformations of simple Lie algebras (1992)
    Springer
    Letters in mathematical physics 24 (1992), S. 63-71 
    Details
    ISSN: 1573-0530
    Keywords: 81S99 ; 57T015
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This Letter examines the question of the structure of the Hopf algebra deformations of the universal enveloping algebras of the simple Lie algebras. Deformations of a complex algebra A are viewed as algebras defined over formal power series rings that specialize to A when the parameters go to 0. Only the case of U(sl(2,C)) is treated but the methods are general. Under the Ansatz that the two Borel subalgebras are deformed as Hopf algebras but possibly differently, we construct a universal two-parameter deformation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00430004
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Universal deformations of reductive Lie algebras (1992)
    Springer
    Letters in mathematical physics 26 (1992), S. 53-65 
    Details
    ISSN: 1573-0530
    Keywords: 81S99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We construct multiparameter quantizations of reductive Lie algebras which have the property of universality within a certain class of deformations. The universal deformations can be defined so that the algebra structure on each simple component is the same as that of the standard one-parameter quantization, the remaining parameters being relegated to the coalgebra structure. We discuss an example in which only the latter parameters appear, as a special case of deformations of a semisimple algebra whose simple components remain classical. Deformations are defined as algebras over power series rings and it is essential to require them to be torsion free to secure the universality. The Poincaré-Birkhoff-Witt theorem and the torsion freeness are established for the universal deformation on the basis of results on the representation theory of the deformed algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00420518
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    Paper (German National Licenses)
    Fulltext
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