caa a22 4500 469099437 CHVBK 20180323133040.0 cr unu---uuuuu 170328e19920901xx s 000 0 eng 10.1007/BF00420518 doi (NATIONALLICENCE)springer-10.1007/BF00420518 Universal deformations of reductive Lie algebras [Elektronische Daten] [P. Truini, V. Varadarajan] 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. Kluwer Academic Publishers, 1992 Truini P. Dipartimento di Fisica, Universitá di Genova, Istituto Nazionale di Fisica Nucleare, v. Dodecaneso 33, 16146, Genova, Italy aut Varadarajan V. Department of Mathematics, University of California, 90024, Los Angeles, CA, USA aut Letters in Mathematical Physics Kluwer Academic Publishers 26/1(1992-09-01), 53-65 0377-9017 26:1<53 1992 26 11005 https://doi.org/10.1007/BF00420518 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00420518 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Truini P. Dipartimento di Fisica, Universitá di Genova, Istituto Nazionale di Fisica Nucleare, v. Dodecaneso 33, 16146, Genova, Italy aut NATIONALLICENCE 700 1- Varadarajan V. Department of Mathematics, University of California, 90024, Los Angeles, CA, USA aut NATIONALLICENCE 773 0- Letters in Mathematical Physics Kluwer Academic Publishers 26/1(1992-09-01), 53-65 0377-9017 26:1<53 1992 26 11005 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer