Results 21 to 30 of about 297,928 (181)
COASSOCIATIVE LIE ALGEBRAS [PDF]
Glasgow Mathematical Journal, 2013 AbstractA coassociative Lie algebra is a Lie algebra equipped with a coassociative coalgebra structure satisfying a compatibility condition. The enveloping algebra of a coassociative Lie algebra can be viewed as a coalgebraic deformation of the usual universal enveloping algebra of a Lie algebra.
Wang, Ding-Guo +2 more
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LIE ALGEBRA PREDERIVATIONS AND STRONGLY NILPOTENT LIE ALGEBRAS [PDF]
Communications in Algebra, 2002 We study Lie algebra prederivations. A Lie algebra admitting a non-singular prederivation is nilpotent. We classify filiform Lie algebras admitting a non-singular prederivation but no non-singular derivation. We prove that any 4-step nilpotent Lie algebra admits a non-singular prederivation.
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Journal of the London Mathematical Society, 1973 Let \(L\) be a finite dimensional Lie algebra over a field. The Frattini subalgebra, \(F(L)\), of \(L\) is the intersection of the maximal subalgebras of \(L\); the Frattini ideal, \(\varphi(L)\), of \(L\) is then the largest ideal of \(L\) contained in \(F(L)\).
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Post-Lie Algebra Structures on the Lie Algebra gl(2,C)
Abstract and Applied Analysis, 2013 The post-Lie algebra is an enriched structure of the Lie algebra. We give a complete classification of post-Lie algebra structures on the Lie algebra gl(2,C) up to isomorphism.
Yuqiu Sheng, Xiaomin Tang
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Lie Bialgebras on the Rank Two Heisenberg–Virasoro Algebra
Mathematics, 2023 The rank two Heisenberg–Virasoro algebra can be viewed as a generalization of the twisted Heisenberg–Virasoro algebra. Lie bialgebras play an important role in searching for solutions of quantum Yang–Baxter equations.
Yihong Su, Xue Chen
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Novikov structures on solvable Lie algebras [PDF]
, 2005 We study Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We show that a Lie algebra admitting a Novikov structure must be solvable.
Bakalov +14 more
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Journal of Algebra, 2001 The authors consider associative algebras with involution. Denote by \(*\) the fixed involution of an associative algebra \(A\) over an algebraically closed field \(\mathbb{F}\) of characteristic zero and denote by \({\mathfrak u}^*(A)\) the vector space of skew-symmetric elements of \(A\) (i.e. \({\mathfrak u}^*(A)=\{a\in A\mid a^*=-a\}\)).
Baranov, AA, Zalesskii, AE
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Nilpotent Lie algebras of derivations with the center of small corank
Karpatsʹkì Matematičnì Publìkacìï, 2020 Let $\mathbb K$ be a field of characteristic zero, $A$ be an integral domain over $\mathbb K$ with the field of fractions $R=Frac(A),$ and $Der_{\mathbb K}A$ be the Lie algebra of all $\mathbb K$-derivations on $A$. Let $W(A):=RDer_{\mathbb K} A$ and $L$
Y.Y. Chapovskyi +2 more
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Lie Algebra Multiplicities [PDF]
Proceedings of the American Mathematical Society, 1979 Exact formulas for root space multiplicities in Cartan matrix Lie algebras and their universal enveloping algebras are computed. We go on to determine the number of free generators of each degree of the radicals defining these algebras.
Berman, Stephen, Moody, Robert V.
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Journal of Algebra, 2002 A Lie algebra is called finitary if it consists of finite-rank linear transformations of a vector space. The authors classify all infinite-dimensional finitary simple Lie algebras over an algebraically closed field of characteristic not 2 or 3. They also do the same for finitary irreducible Lie algebras.
Baranov, A.A., Strade, H.
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