graded algebra

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• Graded algebra — In mathematics, in particular abstract algebra, a graded algebra is an algebra over a field (or commutative ring) with an extra piece of structure, known as a gradation (or grading ). Graded rings A graded ring A is a ring that has a direct sum… …   Wikipedia

• Differential graded algebra — In mathematics, in particular abstract algebra and topology, a differential graded algebra is a graded algebra with an added chain complex structure that respects the algebra structure. Contents 1 Definition 2 Examples of DGAs 3 Other facts about …   Wikipedia

• Graded Lie algebra — In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra is a Lie algebra which is also a nonassociative graded algebra under the bracket… …   Wikipedia

• Graded vector space — In mathematics, a graded vector space is a type of vector space that includes the extra structure of gradation, which is a decomposition of the vector space into a direct sum of vector subspaces. Contents 1 N graded vector spaces 2 General I… …   Wikipedia

• Graded category — A graded category is a mathematical concept.If mathcal{A} is a category, then amathcal{A} graded categoryis a category mathcal{C} together with a functorF:mathcal{C} ightarrow mathcal{A}.Monoids and groups can be thought of categories with a… …   Wikipedia

• Exterior algebra — In mathematics, the exterior product or wedge product of vectors is an algebraic construction generalizing certain features of the cross product to higher dimensions. Like the cross product, and the scalar triple product, the exterior product of… …   Wikipedia

• Filtered algebra — In mathematics, a filtered algebra is a generalization of the notion of a graded algebra. Examples appear in many branches of mathematics, especially in homological algebra and representation theory. A filtered algebra over the field k is an… …   Wikipedia

• Steenrod algebra — In algebraic topology, a branch of mathematics, the Steenrod algebra is a structure occurring in the theory of cohomology operations. It is an object of great importance, most especially to homotopy theorists. More precisely, for a given prime… …   Wikipedia

• Derivation (abstract algebra) — In abstract algebra, a derivation is a function on an algebra which generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K derivation is a K linear map D: A → A that… …   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

• 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