Algebras with one operation including Poisson and other Lie-admissible algebras
نویسندگان
چکیده
منابع مشابه
0 D ec 2 00 4 Algebras with one operation including Poisson and other Lie - admissible algebras
We investigate algebras with one operation. We study when these algebras form a monoidal category and analyze Koszulness and cyclicity of the corresponding operads. We also introduce a new kind of symmetry for operads, the dihedrality , responsible for the existence of dihedral cohomology. The main trick, which we call the polarization, will be to represent an algebra with one operation without...
متن کاملLie-admissible Algebras and Operads
A Lie-admissible algebra gives a Lie algebra by anticommutativity. In this work we describe remarkable types of Lie-admissible algebras such as Vinberg algebras, pre-Lie algebras or Lie algebras. We compute the corresponding binary quadratic operads and study their duality. Considering Lie algebras as Lie-admissible algebras, we can define for each Lie algebra a cohomology with values in an Lie...
متن کاملVertex Lie algebras, vertex Poisson algebras and vertex algebras
The notions of vertex Lie algebra and vertex Poisson algebra are presented and connections among vertex Lie algebras, vertex Poisson algebras and vertex algebras are discussed.
متن کاملOn the Riemann-Lie Algebras and Riemann-Poisson Lie Groups
A Riemann-Lie algebra is a Lie algebra G such that its dual G∗ carries a Riemannian metric compatible (in the sense introduced by the author in C. R. Acad. Sci. Paris, t. 333, Série I, (2001) 763–768) with the canonical linear Poisson structure of G∗ . The notion of Riemann-Lie algebra has its origins in the study, by the author, of Riemann-Poisson manifolds (see Differential Geometry and its A...
متن کاملHom-lie Admissible Hom-coalgebras and Hom-hopf Algebras
The aim of this paper is to generalize the concept of Lie-admissible coalgebra introduced in [2] to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures introduced in [12].
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: Journal of Algebra
سال: 2006
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2005.09.018