The curvature of n-dimensional Riemannian manifold is given by an antisymmetric n×n matrix of 2-forms (or equivalently a 2-form with values in , the Lie algebra of the orthogonal group , which is the structure group of the tangent bundle of a Riemannian manifold).
It is equipped to handle certain non-commutative algebras which are extensively used in theoretical high energy physics: Clifford algebras, SU(3) Lie algebras, and Lorentz tensors.
He is the co-discover of Kac-Moody algebra, a Lie algebra, usually infinite-dimensional, that can be defined through a generalized root system.
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In mathematics, a Kac–Moody algebra (named for Victor Kac and Robert Moody, who independently discovered them) is a Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix.
Nevertheless, particles can indeed be neatly divided into groups that form irreducible representations of the Lie algebra SU(3), as first noted by Murray Gell-Mann and independently by Yuval Ne'eman (see the eightfold way).
He obtained his Ph. D. from Columbia under the guidance of Samuel Eilenberg in Filtered algebras and Representations of Lie Algebras.
Tan Eng Chye’s research interests are Representation Theory of Lie Groups and Lie Algebra and Invariant theory and Algebraic combinatorics.
In geometry, 2k1 polytope is a uniform polytope in n dimensions (n = k+4) constructed from the Coxeter group.
In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the Coxeter group, and having only regular polytope facets.
Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics.
In mathematics, a Lie-* algebra is a D-module with a Lie* bracket.
He introduced the Duflo isomorphism, an isomorphism between the center of the enveloping algebra of a finite-dimensional Lie algebra and the invariants of its symmetric algebra.
A more general subclass consists of the axisymmetric pp-waves, which in general have a two dimensional Abelian Lie algebra of Killing vector fields.
# the normal form (or split form), sp(2n, R), which is the Lie algebra of Sp(2n, R).