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reductive subalgebra

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  • An Exceptionally Simple Theory of Everything — is a preprint proposing a basis for a unified field theory, named E8 Theory , which attempts to describe all known fundamental interactions in physics, and to stand as a possible theory of everything. The preprint was posted to the physics arXiv… …   Wikipedia

  • Cartan connection — In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general concept of a principal connection, in which the …   Wikipedia

  • E₈ — In mathematics, E8 is the name given to a family of closely related structures. In particular, it is the name of four exceptional simple Lie algebras as well as that of the six associated simple Lie groups. It is also the name given to the… …   Wikipedia

  • Haboush's theorem — In mathematics Haboush s theorem, often still referred to as the Mumford conjecture, states that for any semisimple algebraic group G over a field K , and for any linear representation ρ of G on a K vector space V , given v ne;0 in V that is… …   Wikipedia

  • Levi decomposition — In Lie theory and representation theory, the Levi decomposition, discovered by Eugenio Elia Levi (1906), states that any finite dimensional real Lie algebra g is (as a vector space) the direct sum of two significant structural parts; namely,… …   Wikipedia

  • Semisimple Lie algebra — In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e., non abelian Lie algebras mathfrak g whose only ideals are {0} and mathfrak g itself. It is called reductive if it is the sum of a semisimple and an… …   Wikipedia

  • Zonal spherical function — In mathematics, a zonal spherical function or often just spherical function is a function on a locally compact group G with compact subgroup K (often a maximal compact subgroup) that arises as the matrix coefficient of a K invariant vector in an… …   Wikipedia

  • Borel subgroup — In the theory of algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup. For example, in the group GLn (n x n invertible matrices), the subgroup of invertible upper… …   Wikipedia

  • Chevalley–Shephard–Todd theorem — In mathematics, the Chevalley–Shephard–Todd theorem in invariant theory of finite groups states that the ring of invariants of a finite group acting on a complex vector space is a polynomial ring if and only if the group is generated by… …   Wikipedia

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