In mathematics, the symmetric algebra S(V) (also denoted Sym(V)) on a vector space V over a field K is a commutative algebra over K that contains V, and...

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, A  is symmetric ⟺ A = A T . {\displaystyle A{\text{...

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

In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric) matrix is a square matrix whose transpose equals its...

generalization of a symmetric algebra and an exterior algebra: indeed, if V is a (non-graded) R-module, then the graded-symmetric algebra of V with trivial...

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

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...

Pseudovector Spinor Tensor Tensor algebra, Free algebra Tensor contraction Symmetric algebra, Symmetric power Symmetric tensor Mixed tensor Pandey, Divyanshu;...

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group...

the complex Lie algebra. Symmetric spaces are classified as follows. First, the universal cover of a symmetric space is still symmetric, so we can reduce...

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

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

Boolean ring, with symmetric difference as the addition of the ring and intersection as the multiplication of the ring. The symmetric difference is equivalent...

is the free anti-symmetric algebra over R {\displaystyle R} in n {\displaystyle n} -generators and the second ring is the free algebra over R {\displaystyle...

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...

matrix Pseudoinverse Adjugate Transpose Dot product Symmetric matrix Orthogonal matrix Skew-symmetric matrix Conjugate transpose Unitary matrix Hermitian...

establishes a duality between the derived category of a symmetric algebra and that of an exterior algebra, as well as the BGG correspondence, which links the...

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

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

λ contains no nonzero left ideal of A. A Frobenius algebra is called symmetric if σ is symmetric, or equivalently λ satisfies λ(a·b) = λ(b·a). There...

tensor product of n single-particle Hilbert spaces H (see symmetric algebra and exterior algebra respectively). A general state in Fock space is a linear...

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...

spectra such as the category of symmetric spectra. Wikibooks has a book on the topic of: Abstract Algebra/Rings Algebra over a commutative ring Categorical...

the theory of holonomy; or algebraically through Lie theory, which allowed Cartan to give a complete classification. Symmetric spaces commonly occur in...

tensor algebra can be constructed as quotients: these include the exterior algebra, the symmetric algebra, the Clifford algebra, the Weyl algebra, and the...

In mathematics, the n-fold symmetric product of an algebraic curve C is the quotient space of the n-fold cartesian product C × C × ... × C or Cn by the...

properties. All Casimir operators correspond to symmetric homogeneous polynomials in the symmetric algebra of the adjoint representation ad g . {\displaystyle...

Group ring Localization of a ring Tensor algebra Symmetric algebra, Exterior algebra, Clifford algebra Free algebra Completion (ring theory) Types Field (mathematics)...

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