Infinite Dimensional Lie Superalgebras

Frobenius extensions of subalgebras of Hopf algebras

“…([BMPZ,p.85]). Assume that char k = 2, 3 and let X = X + ∪X − be a G-homogeneous basis of the G-Lie coloralgebra L. Then the universal enveloping algebra U (L) has a G-homogeneous basis over k consisting of 1 and all monomials of the form y…”

Deformations of quantum hyperplanes

“…For the case of (colour) Lie algebras 9 (see, e.g., [1]) this theorem provides us with a basis of the universal enveloping algebra U(fl) of g. It is well known that in this case the PBW theorem is equivalent to Jacobi's identity.…”

“…The cohomology in [1][2][3][4] is Hochschild cohomology, whereas our cohomology is related to cohomology of the underlying linear space, as in Lie algebra theory; in particular for low dimensions the cohomology is easy to compute.…”

Algebra of Skew-Primitive Elements

“…It is easy to see that the above operation satisfies the identities ) is a Lie (G, λ)-color superalgebra, where G is a subgroup of G * × G, generated by elements of the form χ a × g a , and the bicharacter is defined by λ(χ × g, χ ′ × g ′ ) = χ(g ′ ), while the symmetry of that bicharacter is implied by the fact that the main operation is total. A standard and well-known argument will show that in the case of characteristic 0, H is itself a universal enveloping algebra of Λ; see, e.g., [13].…”