which is a graded vector space (or a graded module). It is not an algebra, as the tensor product of two symmetric tensors is not symmetric in general...

Alternating multilinear map Exterior algebra Graded-symmetric algebra Supercommutative algebra Nicolas Bourbaki (1998). Algebra I. Springer Science+Business Media...

In algebra, given a commutative ring R, the graded-symmetric algebra of a graded R-module M is the quotient of the tensor algebra of M by the ideal I generated...

is also a graded ring is called a graded algebra. A graded ring could also be viewed as a graded ⁠ Z {\displaystyle \mathbb {Z} } ⁠-algebra. The associativity...

differential graded commutative algebra". arXiv:1307.0369 [math.AC]. DG algebra graded-symmetric algebra alternating algebra supercommutative algebra v t e...

In algebra and in particular in algebraic combinatorics, the ring of symmetric functions is a specific limit of the rings of symmetric polynomials in...

Multilinear algebra Symmetric algebra, the symmetric analog Tensor algebra Weyl algebra, a quantum deformation of the symmetric algebra by a symplectic...

homological algebra, algebraic topology, and algebraic geometry – a differential graded algebra (or DGA, or DG algebra) is an algebraic structure often...

characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric algebra on V. A related concept is...

Functional-theoretic algebra Genetic algebra Geometric algebra Gerstenhaber algebra Graded algebra Griess algebra Group algebra Group algebra of a locally compact...

axioms for Boolean algebra Peirce arrow Read-once function Sheffer stroke Sole sufficient operator Symmetric Boolean function Symmetric difference Zhegalkin...

geometric algebra (also known as a Clifford algebra) is an algebra that can represent and manipulate geometrical objects such as vectors. Geometric algebra is...

tensor algebra is important because many other algebras arise as quotient algebras of T(V). These include the exterior algebra, the symmetric algebra, Clifford...

finite-dimensional, graded commutative, graded cocommutative Hopf algebra over a field of characteristic 0. Then A {\displaystyle A} (as an algebra) is a free...

anti-symmetrizing, so the algebra decomposes as a direct sum of modules (vector spaces if the *-ring is a field) of symmetric and anti-symmetric (Hermitian and skew...

example, a graded Lie algebra is a Lie algebra (or more generally a Lie superalgebra) with a compatible grading. A differential graded Lie algebra also comes...

the exterior algebra, in the same way that the Weyl algebra is a quantization of the symmetric algebra. Weyl algebras and Clifford algebras admit a further...

forms an associative K-algebra. The product {, }, called the Poisson bracket, forms a Lie algebra, and so it is anti-symmetric, and obeys the Jacobi identity...

supersymmetry algebras (without central charges or internal symmetries), and are Lie superalgebras. Thus a super-Poincaré algebra is a Z2-graded vector space...

equipped with a nonsingular real symmetric bilinear form ( ⋅ , ⋅ ) {\displaystyle (\cdot ,\cdot )} instead, the unital *-algebra generated by the elements of...

mathematics and theoretical physics, a superalgebra is a Z2-graded algebra. That is, it is an algebra over a commutative ring or field with a decomposition...

it is a graded algebra, with the graded piece of weight k being called the k-th exterior power of V. Symmetric power, symmetric algebra This is the invariant...

unit of the universal enveloping algebra (called 1 above). The algebra W(V) is a quantization of the symmetric algebra Sym(V). If V is over a field of...

generalization of the notion of Riemannian symmetric space from real manifolds to complex manifolds. Every Hermitian symmetric space is a homogeneous space for...

S_{m}{\mathfrak {g}}} of symmetric tensor products Sym m ⁡ g {\displaystyle \operatorname {Sym} ^{m}{\mathfrak {g}}} . Its limit is the symmetric algebra S ( g ) {\displaystyle...

finite symmetric groups Sn, and is a non-commutative analogue of the Hopf algebra of symmetric functions. It is both free as an algebra and graded-cofree...

the monster Lie algebra. Finite-dimensional semisimple Lie algebras have the following properties: They have a nondegenerate symmetric invariant bilinear...

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice. This type of algebraic structure captures essential properties...

characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric algebra on V. A related concept is...

In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms: x y = y x {\displaystyle...