Graded vector space information

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...

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

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

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

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

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...

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...

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...

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...

\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...

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...

) Category of rings Derived category Module spectrum Category of graded vector spaces Category of abelian groups Category of representations Change of...

differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. A differential graded algebra...

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...

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...

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...

Lie algebras. Graded algebra: a graded vector space with an algebra structure compatible with the grading. The idea is that if the grades of two elements...

link L, we assign the Khovanov bracket [D], a cochain complex of graded vector spaces. This is the analogue of the Kauffman bracket in the construction...

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...

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...

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

{\displaystyle (A^{\bullet },m_{i})} is a Z {\displaystyle \mathbb {Z} } -graded vector space over a field k {\displaystyle k} with a series of operations m i...

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...