Enveloping Algebras of Certain Types of Color Hom-Lie Algebras

Simply Complete Hom-Lie Superalgebras and Decomposition of Complete Hom-Lie Superalgebras

“…The Hom-Lie superalgebras and the more general color quasi-Lie algebras provide new general parametric families of non-associative structures, extending and interpolating on the fundamental level of defining identities between the Lie algebras, Lie superalgebras, color Lie algebras and some other important related non-associative structures, their deformations and discretizations, in the special interesting ways which may be useful for unification of models of classical and quantum physics, geometry and symmetry analysis, and also in algebraic analysis of computational methods and algorithms involving linear and non-linear discretizations of differential and integral calculi. Investigation of color hom-Lie algebras and hom-Lie superalgebras and n-ary generalizations have been further expanded recently in [1,2,7,8,[11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]33,42,43,[48][49][50]60,61,64,65,[69][70][71][72][73]75].…”

HNN-extension of involutive multiplicative Hom-Lie algebras

“…This construction leads to a Poincare-Birkhoff-Witt theorem for the enveloping associative algebra of an involutive Hom-Lie algebra. This approach has been extended to the enveloping algebras for color Hom-Lie algebras in [11,12]. Extensions of Hom-Lie superalgebras and Hom-Lie color algebras have been considered in [9,13].…”