Quasi-Lie algebras, quasi-Lie central extensions and quasi-deformations
of Lie and color Lie algebras.
In this talk the class of quasi-Lie algebras and some of its subclasses
will be presented, including general construction methods and examples
coming from twisted derivations and twisted generalized vector fields,
color Lie algebras, generalized quasi-Lie central extensions of Lie
algebras and superalgebras. Among examples arising within quasi-Lie
algebras framework are known and new one-parameter and multi-parameter
deformations of infinite-dimensional Lie algebras of Witt and Virasoro
type some of which appear in the context of conformal field theory,
string theory and deformed vertex models, multi-parameter families of
quadratic and almost quadratic algebras that include for special natural
choices of parameters algebras appearing in non-commutative algebraic
geometry, as well as universal enveloping algebras of Lie algebras, Lie
superalgebras and color Lie algebras. Common uniting feature for all
these algebras is appearance of twisted generalizations of Jacoby
identities providing new structures of interest for investigation from
the side of associative algebras, the non-associative algebras, twisted
generalizations of Hopf algebras, the non-commutative differential
calculi beyond usual differential calculus and generalized central and
other (co-)homological extensions.
 D. Larsson, S. Silvestrov, Quasi-Lie algebras, in "Noncommutative
Geometry and Representation Theory in Mathematical Physics", AMS,
Contemporary Mathematics, Vol. 391, 2005, 7 pp .
 J. Hartwig, D. Larsson, S. Silvestrov, Deformations of Lie algebras
using sigma-derivations, J. Algebra 295 (2006), no. 2, 314-361.
 D. Larsson, S. Silvestrov, Quasi-hom-Lie Algebras, Central
Extensions and 2-cocycle-like Identities, J. Algebra 288 (2005), no. 2,
 D. Larsson, S. Silvestrov, Quasi-deformations of sl(2,K) using
twisted derivations, Communications in Algebra, 35, 2007, 4303-4318.