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 کاملDomestic Canonical Algebras and Simple Lie Algebras
For each simply-laced Dynkin graph ∆ we realize the simple complex Lie algebra of type ∆ as a quotient algebra of the complex degenerate composition Lie algebra L(A) 1 of a domestic canonical algebra A of type ∆ by some ideal I of L(A) 1 that is defined via the Hall algebra of A, and give an explicit form of I. Moreover, we show that each root space of L(A) 1 /I has a basis given by the coset o...
متن کاملSimple Lie Algebras Which Generalize Witt Algebras
We introduce a new class of simple Lie algebras W (n, m) (see Definition 1) that generalize the Witt algebra by using " exponential " functions, and also a subalgebra W * (n, m) thereof; and we show each derivation of W * (1, 0) can be written as a sum of an inner derivation and a scalar derivation (Theorem. 2) [10]. The Lie algebra W (n, m) is Z-graded and is infinite growth [4].
متن کاملProjectivity and isomorphism of strictly simple algebras
We describe a sufficient condition for the localization functor to be a categorical equivalence. Using this result we explain how to simplify the test for projectivity. This leads to a description of the strictly simply algebras which are projective in the variety they generate. A byproduct of our efforts is the result that if A and B are strictly simple and generate the same variety, then A$B ...
متن کاملCanonical Isomorphism of Two Lie Algebras Arising in CR-geometry
A CR-structure on a smooth real manifold M of dimension m is a smooth distribution of subspaces in the tangent spaces T c p (M) ⊂ Tp(M), p ∈ M , with operators of complex structure Jp : T c p (M) → T c p (M), J 2 p ≡ −id, that depend smoothly on p. A manifold M equipped with a CR-structure is called a CR-manifold. It follows that the number CRdimM := dimCT c p (M) does not depend on p; it is ca...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1973
ISSN: 0002-9947
DOI: 10.2307/1996590