Cluster algebras are a class of commutative rings introduced by Fomin and Zelevinsky (2002, 2003, 2007). A cluster algebra of rank n is an integral domain...

complete graphs Clusterable graph, in balance theory Cluster algebra, a class of commutative rings used in representation theory Cluster expansion, a technique...

Birman–Wenzl algebra Boolean algebra Borcherds algebra Brauer algebra C*-algebra Central simple algebra Clifford algebra Cluster algebra Dendriform algebra Differential...

its relations with algebra, geometry, and representation theory. Together with Andrei Zelevinsky, he introduced cluster algebras. Fomin received his...

is an American mathematician known for her work on cluster algebras, tropical geometry, algebraic combinatorics, amplituhedra, and the positive Grassmannian...

copies of K we associate the identity map. This theory was related to cluster algebras by Derksen, Weyman, and Zelevinsky. To enforce commutativity of some...

Zelevinsky's most notable achievement is the discovery (with Sergey Fomin) of cluster algebras. His other contributions include: Bernstein–Zelevinsky classification...

(Jordan algebra), an operation on Jordan algebras that creates different Jordan algebras Mutation of a seed, in the theory of cluster algebras Apophony...

basic rule to let the labels propagate dynamically. Max Glick used the cluster algebra formalism to find formulas for the iterates of the pentagram map in...

triangulated Calabi–Yau categories to the (additive) categorification of cluster algebras. In 2013, he received an honorary degree from the University of Antwerp...

areas of cluster algebras, representation theory of finite-dimensional algebras, homological algebra, tilting theory, quantum groups, algebraic groups,...

{\displaystyle A_{3}} root system, and the A 3 {\displaystyle A_{3}} cluster algebra. The connection with the associahedron provides a correspondence between...

decomposition for affine groups. Cluster algebra This Week's Finds in Mathematical Physics, Week 186 Borel, Armand. Linear Algebraic Groups (2nd ed.). New York:...

21st century, new relations were found between frieze patterns and cluster algebras, Grassmannians, linear difference equations, moduli spaces of points...

associated to a hereditary algebra A. A cluster tilted algebra arises from a tilted algebra as a certain semidirect product, and the cluster category of A summarizes...

in the mathematical fields algebra, representation theory, cluster algebras, cluster categories, combinatorics, Lie algebras. Currently she is a professor...

Titular C. His research deals with cluster algebras in Lie theory and their categorization, pre-projective algebras, and quivers in combination with symmetrizable...

mathematician working in noncommutative algebra, representation theory, Artin algebras, and cluster algebras. She is a professor of mathematics at Northeastern...

f(g)=f(hgh^{-1})} ; it is a function on conjugacy classes. cluster algebra A cluster algebra is an integral domain with some combinatorial structure on...

Witt vectors Hecke algebra (used in Wiles's proof of Fermat's Last Theorem) Fontaine's period rings Cluster algebra Convolution algebra (of a commutative...

dilogarithm finds applications in mathematical physics, quantum topology, cluster algebra theory. The precise relationship between the q-exponential and Φ b...

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

many contributions to algebra and algebraic topology, and in particular for his pioneering work in homological and categorical algebra. 1985 Michael Spivak...

specifies that a certain type of event, namely a tail event of independent σ-algebras, will either almost surely happen or almost surely not happen; that is...

cyclohedron belongs to the generalized associahedra that arise from cluster algebra, and to the graph-associahedra, a family of polytopes each corresponding...

mathematics, the Virasoro algebra is a complex Lie algebra and the unique nontrivial central extension of the Witt algebra. It is widely used in two-dimensional...

Richard P. Stanley Distinguished University Professor; introduced Cluster algebra with Andrei Zelevinsky; mentored Fields medalist June Huh William Fulton...

educator and academic administrator Bethany Rose Marsh, British expert in cluster algebras and tilting theory Susan H. Marshall, American number theorist Maia...

In multivariate statistics, spectral clustering techniques make use of the spectrum (eigenvalues) of the similarity matrix of the data to perform dimensionality...

the Somos sequences; it is closely related to the combinatorics of cluster algebras. For k ≥ 8 the analogously defined sequences eventually contain fractional...