mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a...

In mathematics, a super vector space is a Z 2 {\displaystyle \mathbb {Z} _{2}} -graded vector space, that is, a vector space over a field K {\displaystyle...

gradation or grading. A graded module is defined similarly (see below for the precise definition). It generalizes graded vector spaces. A graded module that...

abstract algebra and topology, a differential graded Lie algebra (or dg Lie algebra, or dgla) is a graded vector space with added Lie algebra and chain complex...

on the above sorts of vectors. A vector space formed by geometric vectors is called a Euclidean vector space, and a vector space formed by tuples is called...

differential graded Lie algebra (or DGLA) is a differential graded analogue of a Lie algebra. That is, it is a differential graded vector space, ( L ∙ , d...

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied...

V=\bigoplus _{i\in I}V_{i}} of spaces. A graded linear map is a map between graded vector spaces respecting their gradations. A graded ring is a ring that is...

In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes...

this graded vector space: V ∙ = ⨁ m ∈ Z V m {\displaystyle V_{\bullet }=\bigoplus _{m\in \mathbb {Z} }V_{m}} A differential graded vector space or chain...

The suspension S V {\displaystyle SV} of a graded vector space V {\displaystyle V} is the graded vector space defined by ( S V ) i = V i + 1 {\displaystyle...

{\displaystyle V\otimes W} of two vector spaces V {\displaystyle V} and W {\displaystyle W} (over the same field) is a vector space to which is associated a bilinear...

inductive hypothesis. An example of graded vector space is associated to a chain complex, or cochain complex C of vector spaces; the latter takes the form 0...

In mathematics, an anyonic Lie algebra is a U(1) graded vector space L {\displaystyle L} over C {\displaystyle \mathbb {C} } equipped with a bilinear...

) Category of rings Derived category Module spectrum Category of graded vector spaces Category of representations Change of rings Morita equivalence stable...

meanings Graded poset, a partially ordered set equipped with a rank function, sometimes called a ranked poset Graded vector space, a vector space with an...

In mathematics, the exterior algebra or Grassmann algebra of a vector space V {\displaystyle V} is an associative algebra that contains V , {\displaystyle...

of a Lie superalgebra is an action of Lie superalgebra L on a Z2-graded vector space V, such that if A and B are any two pure elements of L and X and...

\bigoplus _{n=0}^{\infty }\operatorname {Sym} ^{n}(V),} which is a graded vector space (or a graded module). It is not an algebra, as the tensor product of two...

or a module is a special case of the Hilbert–Poincaré series of a graded vector space. The Hilbert polynomial and Hilbert series are important in computational...

over that coalgebra. A graded vector space V can be made into a comodule. Let I be the index set for the graded vector space, and let C I {\displaystyle...

Lie superalgebras. Thus a super-Poincaré algebra is a Z2-graded vector space with a graded Lie bracket such that the even part is a Lie algebra containing...

field is of characteristic zero is made. A homotopy Lie algebra on a graded vector space V = ⨁ V i {\displaystyle V=\bigoplus V_{i}} is a continuous derivation...

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...

polynomials of degree r on V. Over fields of characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric...

bracket [ D ] {\displaystyle \left[D\right]} , a cochain complex of graded vector spaces. This is the analogue of the Kauffman bracket in the construction...

{Z} } ⁠-graded vector space to ⁠ Z 2 {\displaystyle \mathrm {Z} _{2}} ⁠-graded vector space. The geometric product respects this coarser grading. Thus in...

elements of a complex vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight...

the property d 2 = 0 {\displaystyle d^{2}=0} . In other words, the graded vector space Ω X ∗ ( E ) {\displaystyle \Omega _{X}^{*}(E)} is a cochain complex...

ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the vector space operations...