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graded subalgebra

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  • Radical polynomial — In mathematics, in the realm of abstract algebra, a radical polynomial is a multivariate polynomial over a field that can be expressed as a polynomial in the sum of squares of the variables. That is, if :k [x 1, x 2,ldots, x n] is a polynomial… …   Wikipedia

  • Clifford algebra — In mathematics, Clifford algebras are a type of associative algebra. They can be thought of as one of the possible generalizations of the complex numbers and quaternions.[1][2] The theory of Clifford algebras is intimately connected with the… …   Wikipedia

  • Spinor — In mathematics and physics, in particular in the theory of the orthogonal groups (such as the rotation or the Lorentz groups), spinors are elements of a complex vector space introduced to expand the notion of spatial vector. Unlike tensors, the… …   Wikipedia

  • Generalized Kac–Moody algebra — In mathematics, a generalized Kac–Moody algebra is a Lie algebra that is similar to a Kac–Moody algebra, except that it is allowed to have imaginary simple roots. Generalized Kac–Moody algebras are also sometimes called GKM… …   Wikipedia

  • Depth of noncommutative subrings — In ring theory and Frobenius algebra extensions, fields of mathematics, there is a notion of depth two subring or depth of a Frobenius extension. The notion of depth two is important in a certain noncommutative Galois theory, which generates Hopf …   Wikipedia

  • Non-associative algebra — This article is about a particular non associative structure known as a non associative algebra. See also the article about non associativity in general. A non associative algebra[1] (or distributive algebra) over a field (or a ring) K is a K… …   Wikipedia

  • Lie superalgebra — In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2 grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry. In most of these theories,… …   Wikipedia

  • Poincaré–Birkhoff–Witt theorem — In the theory of Lie algebras, the Poincaré–Birkhoff–Witt theorem (Poincaré (1900), G. D. Birkhoff (1937), Witt (1937); frequently contracted to PBW theorem) is a result giving an explicit description of the universal enveloping algebra of a Lie… …   Wikipedia

  • Free Lie algebra — In mathematics, a free Lie algebra, over a given field K, is a Lie algebra generated by a set X, without any imposed relations. Contents 1 Definition 2 Universal enveloping algebra 3 Hall sets …   Wikipedia

  • Noncommutative geometry — Not to be confused with Anabelian geometry. Noncommutative geometry (NCG) is a branch of mathematics concerned with geometric approach to noncommutative algebras, and with construction of spaces which are locally presented by noncommutative… …   Wikipedia

  • Symmetric algebra — In mathematics, the symmetric algebra S ( V ) (also denoted Sym ( V )) on a vector space V over a field K is the free commutative unital associative K algebra containing V .It corresponds to polynomials with indeterminates in V , without choosing …   Wikipedia

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