In algebra, a Lie-admissible algebra, introduced by A. Adrian Albert (1948), is a (possibly non-associative) algebra that becomes a Lie algebra under the...

ab − ba. Examples include alternative algebras, Malcev algebras and Lie-admissible algebras. Jordan-admissible algebra Albert, A. Adrian (1948), "Power-associative...

algebra that becomes a Jordan algebra under the product a ∘ b = ab + ba. Malcev-admissible algebra Lie-admissible algebra Okubo 1995, pp. 19, 84 Albert...

In mathematics, an admissible algebra is a (possibly non-associative) commutative algebra whose enveloping Lie algebra of derivations splits into the...

Lie groups, Lie algebras and their representation theory, a Lie algebra extension e is an enlargement of a given Lie algebra g by another Lie algebra...

In mathematics, a Malcev algebra (or Maltsev algebra or Moufang–Lie algebra) over a field is a nonassociative algebra that is antisymmetric, so that x...

studied by Susumu Okubo. Okubo algebras are composition algebras, flexible algebras (A(BA) = (AB)A), Lie admissible algebras, and power associative, but...

matrix multiplication). The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras. The most prominent of these...

reductive Lie groups. All irreducible unitary representations are admissible (or rather their Harish-Chandra modules are), and the admissible representations...

mathematics, admissible representations are a well-behaved class of representations used in the representation theory of reductive Lie groups and locally...

algebra, or Hecke algebra, named for Erich Hecke and Nagayoshi Iwahori, is a deformation of the group algebra of a Coxeter group. The Hecke algebra can...

is Lie-admissible. If A is alternative then so is any homotope of A, and any mutation of A is Malcev-admissible. Any isotope of a Hurwitz algebra is isomorphic...

basis H, X, Y for the complexification of the Lie algebra of SL(2, R) so that iH generates the Lie algebra of a compact Cartan subgroup K (so in particular...

classification. One of these describes the irreducible admissible (g, K)-modules, for g a Lie algebra of a reductive Lie group G, with maximal compact subgroup K,...

In the mathematical study of Lie algebras and Lie groups, Satake diagrams are a generalization of Dynkin diagrams that classify involutions of root systems...

related to C2-cofiniteness. A vertex operator algebra V {\displaystyle V} is rational if the category of admissible modules is semisimple and there are only...

to be admissible if it is guaranteed to return an optimal solution. If the heuristic function used by A* is admissible, then A* is admissible. An intuitive...

over any algebraically closed field. In particular, the simple algebraic groups are classified by Dynkin diagrams, as in the theory of compact Lie groups...

the inner product on W, the Lie algebra of G, and the direct sum decomposition of the Lie algebra of G into the Lie algebra of K and W. This reduces the...

complex Lie algebras. Dimension 0: The only Lie algebra is the abelian Lie algebra R0. Dimension 1: The only Lie algebra is the abelian Lie algebra R1, with...

Roberts) Hahn–Mal'cev–Neumann series Malcev algebra Mal'cev's criterion Malcev Lie algebra Malcev-admissible algebra Mostowski, Andrzej (1969). "Review: Model...

intermediate between Lie groups (or algebraic groups) and Lie algebras. They are used in algebraic number theory and algebraic topology. A one-dimensional...

and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind...

In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given...

(2006). A General Computational Scheme for Testing Admissibility of Nilpotent Orbits of Real Lie Groups of Inner Type. Mathematical Software - ICMS 2006...

representation of a semisimple Lie algebra. In Weyl's approach to the representation theory of connected compact Lie groups, the proof of the character...

In algebraic geometry, motives (or sometimes motifs, following French usage) is a theory proposed by Alexander Grothendieck in the 1960s to unify the...

smooth admissible representations of interest as the local components of automorphic representations of the group of units of a division algebra over a...

about Lie groups can be converted to purely algebraic questions about Lie algebras and then solved. An example of a topological group that is not a Lie group...

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space...