Locally conformally balanced metrics on almost abelian Lie algebras
نویسندگان
چکیده
Abstract We study locally conformally balanced metrics on almost abelian Lie algebras, namely solvable algebras admitting an ideal of codimension one, providing characterizations in every dimension. Moreover, we classify six-dimensional and some compatibility results between different types special Hermitian groups their compact quotients. end by classifying hyperkähler structures.
منابع مشابه
Abelian Complex Structures on Solvable Lie Algebras
We obtain a characterization of the Lie algebras admitting abelian complex structures in terms of certain affine Lie algebras aff(A), where A is a commutative algebra.
متن کاملLie Algebras with Abelian Centralizers
We classify all finite dimensional Lie algebras over an algebraically closed field of characteristic 0, whose nonzero elements have abelian centralizers. These algebras are either simple or solvable, where the only simple such Lie algebra is sl2. In the solvable case they are either abelian or a one-dimensional split extension of an abelian Lie algebra.
متن کاملRealization of locally extended affine Lie algebras of type $A_1$
Locally extended affine Lie algebras were introduced by Morita and Yoshii in [J. Algebra 301(1) (2006), 59-81] as a natural generalization of extended affine Lie algebras. After that, various generalizations of these Lie algebras have been investigated by others. It is known that a locally extended affine Lie algebra can be recovered from its centerless core, i.e., the ideal generated by weight...
متن کاملLie $^*$-double derivations on Lie $C^*$-algebras
A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...
متن کاملAlmost Integral Tqfts from Simple Lie Algebras
Almost integral TQFT was introduced by Gilmer [G]. For each simple Lie algebra g and some prime integer we associate an almost integral TQFT which derives the projective Witten-Reshetikhin-Turaev invariant τ for closed 3-manifolds. As a corollary, one can show that τ is an algebraic integer for certain prime integers. The result in this paper can be used to prove that τ M satisfies some Murasug...
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: Complex Manifolds
سال: 2021
ISSN: ['2300-7443']
DOI: https://doi.org/10.1515/coma-2020-0111