In mathematics, the Hall algebra is an associative algebra with a basis corresponding to isomorphism classes of finite abelian p-groups. It was first discussed...

In mathematics, a Ringel–Hall algebra is a generalization of the Hall algebra, studied by Claus Michael Ringel (1990). It has a basis of equivalence classes...

Genetic algebra Geometric algebra Gerstenhaber algebra Graded algebra Griess algebra Group algebra Group algebra of a locally compact group Hall algebra Hecke...

Linear algebra is the branch of mathematics concerning linear equations such as a 1 x 1 + ⋯ + a n x n = b , {\displaystyle a_{1}x_{1}+\cdots +a_{n}x_{n}=b...

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

defined indirectly by Philip Hall using the Hall algebra, and later defined directly by Dudley E. Littlewood (1961). The Hall–Littlewood polynomial P is...

Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...

an algebra A over a field F is an algebra homomorphism from A to F, or equivalently, a one-dimensional representation of A over F. It is the algebra analogue...

Hall algebra, and Hall polynomials Hall subgroup Hall–Higman theorem Hall–Littlewood polynomial Hall's universal group Hall's marriage theorem Hall word...

In mathematics, Lie group–Lie algebra correspondence allows one to correspond a Lie group to a Lie algebra or vice versa, and study the conditions for...

including those of Hall, Rossmann, and Stillwell. Restricting attention to matrix Lie groups simplifies the definition of the Lie algebra and the exponential...

applications in physics. They also introduced the notion of Cohomological Hall algebra which has numerous applications in geometric representation theory and...

In mathematics, a free Lie algebra over a field K is a Lie algebra generated by a set X, without any imposed relations other than the defining relations...

representation theory of semisimple Lie algebras is one of the crowning achievements of the theory of Lie groups and Lie algebras. The theory was worked out mainly...

representation theory, a Lie algebra representation or representation of a Lie algebra is a way of writing a Lie algebra as a set of matrices (or endomorphisms...

enveloping algebra of a Lie algebra is the unital associative algebra whose representations correspond precisely to the representations of that Lie algebra. Universal...

represent the groups. In Cartan's classification of the simple Lie algebras, the Lie algebra of the complex group Sp(2n, C) is denoted Cn, and Sp(n) is the...

Borel sets on X forms a σ-algebra, known as the Borel algebra or Borel σ-algebra. The Borel algebra on X is the smallest σ-algebra containing all open sets...

In mathematics, specifically algebraic geometry, Donaldson–Thomas theory is the theory of Donaldson–Thomas invariants. Given a compact moduli space of...

This (real) Lie algebra has dimension n2 − 1. More information about the structure of this Lie algebra can be found below in § Lie algebra structure. In...

In mathematics and theoretical computer science, a Kleene algebra (/ˈkleɪni/ KLAY-nee; named after Stephen Cole Kleene) is a semiring that generalizes...

In algebra, the kernel of a homomorphism is the relation describing how elements in the domain of the homomorphism become related in the image. A homomorphism...

In mathematics, a ring is an algebraic structure consisting of a set with two binary operations called addition and multiplication, which obey the same...

algebras Adjoint representation of a Lie group List of Lie group topics Symmetry in quantum mechanics Wigner D-matrix Hall 2015 Corollary 3.51 Hall 2015...

Polyeder unter Einschluss der Elemente der Topologie, by Hans Rademacher. Hall algebra Hauptvermutung Medial graph Steinitz class Steinitz exchange lemma Supernatural...

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

of mathematics known as universal algebra (and in its applications), a subdirectly irreducible algebra is an algebra that cannot be factored as a subdirect...

In mathematics, the structure constants or structure coefficients of an algebra over a field are the coefficients of the basis expansion (into linear combination...

is a nilpotent subalgebra h {\displaystyle {\mathfrak {h}}} of a Lie algebra g {\displaystyle {\mathfrak {g}}} that is self-normalising (if [ X , Y...