The dimension subalgebra problem for enveloping algebras of Lie superalgebras
نویسندگان
چکیده
منابع مشابه
The Isomorphism Problem for Universal Enveloping Algebras of Lie Algebras
Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) ∼= U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.
متن کاملOn dimension of a special subalgebra of derivations of nilpotent Lie algebras
Let $L$ be a Lie algebra, $mathrm{Der}(L)$ be the set of all derivations of $L$ and $mathrm{Der}_c(L)$ denote the set of all derivations $alphainmathrm{Der}(L)$ for which $alpha(x)in [x,L]:={[x,y]vert yin L}$ for all $xin L$. We obtain an upper bound for dimension of $mathrm{Der}_c(L)$ of the finite dimensional nilpotent Lie algebra $L$ over algebraically closed fields. Also, we classi...
متن کاملEnveloping Algebras of Hom-lie Algebras
A Hom-Lie algebra is a triple (L, [−,−], α), where α is a linear self-map, in which the skew-symmetric bracket satisfies an α-twisted variant of the Jacobi identity, called the Hom-Jacobi identity. When α is the identity map, the Hom-Jacobi identity reduces to the usual Jacobi identity, and L is a Lie algebra. Hom-Lie algebras and related algebras were introduced in [1] to construct deformation...
متن کاملPrimeness of the Enveloping Algebra of the Special Lie Superalgebras
A primeness criterion due to Bell is shown to apply to the universal enveloping algebra of the Cartan type Lie superal-gebras S(V) and e S(V ; t) when dim V is even. This together with other recent papers yields Theorem. Let L be a nite-dimensional simple Lie superalgebra over an algebraically closed eld of characteristic zero. Then L satisses Bell's criterion (so that U(L) is prime), unless L ...
متن کاملGröbner-Shirshov Bases for Lie Superalgebras and Their Universal Enveloping Algebras
We show that a set of monic polynomials in the free Lie superalgebra is a Gröbner-Shirshov basis for a Lie superalgebra if and only if it is a Gröbner-Shirshov basis for its universal enveloping algebra. We investigate the structure of GröbnerShirshov bases for Kac-Moody superalgebras and give explicit constructions of Gröbner-Shirshov bases for classical Lie superalgebras. Supported in part by...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1995
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1995-1264829-0