mathematics, the noncommutative symmetric functions form a Hopf algebra NSymm analogous to the Hopf algebra of symmetric functions. The Hopf algebra...

The chromatic symmetric function is a symmetric function invariant of graphs studied in algebraic graph theory, a branch of mathematics. It is the weight...

quasisymmetric functions is the ring of noncommutative symmetric functions. Every symmetric function is also a quasisymmetric function, and hence the...

symmetry. Examples include even and odd functions in calculus, symmetric groups in abstract algebra, symmetric matrices in linear algebra, and Galois groups...

In mathematics, noncommutative harmonic analysis is the field in which results from Fourier analysis are extended to topological groups that are not commutative...

certain classes of noncommutative rings in a geometric fashion as if they were rings of functions on (non-existent) 'noncommutative spaces'. This trend...

Hazewinkel, Michiel (January 2003). "Symmetric Functions, Noncommutative Symmetric Functions, and Quasisymmetric Functions". Acta Applicandae Mathematicae...

By analogy with the commutative case, the noncommutative symmetric polynomials f are the noncommutative polynomials of the form f = fT. When any real...

of noncommutative determinants, also known as quasideterminants Introduction of noncommutative symmetric functions The introduction of noncommutative Plücker...

{NSymm} =\mathbf {Z} \langle Z_{1},Z_{2},\ldots \rangle } of noncommutative symmetric functions in countably many variables Z1, Z2, ...: the part D i : A...

MR 0693308 Connes, Alain (1999), "Trace formula in noncommutative geometry and the zeros of the Riemann zeta function", Selecta Mathematica, New Series, 5 (1):...

A = AT, is a symmetric matrix. If instead, A is equal to the negative of its transpose, that is, A = −AT, then A is a skew-symmetric matrix. In complex...

combinatorics, the theory of noncommutative symmetric functions, the theory of polynomials over division rings, and noncommutative geometry. Several of the...

transform of a real-valued function ( f R E + f R O ) {\displaystyle (f_{_{RE}}+f_{_{RO}})} is the conjugate symmetric function f ^ R E + i   f ^ I O . {\displaystyle...

Proceedings of the AMS Special Session on Representation Theory and Noncommutative Harmonic Analysis, held in memory of Harish-Chandra on the occasion...

ISBN 978-1-61197-723-3. Retrieved 2024-08-12. Brešar, Matej (2014). Introduction to Noncommutative Algebra. Springer. ISBN 978-3-319-08693-4. Retrieved 2024-06-14. Brown...

weak* dense subset of the fully symmetric traces on a general fully symmetric ideal. It is known the fully symmetric traces are a strict subset of the...

occurrence of a variable is used at most once”. Ordered types correspond to noncommutative logic where exchange, contraction and weakening are discarded. This...

Connes, Alain (1999). "Trace formula in noncommutative geometry and the zeros of the Riemann zeta function". Selecta Mathematica. 5: 29–106. arXiv:math/9811068...

algebraic variety, and the ring of integers of a number field. Examples of noncommutative rings include the ring of n × n real square matrices with n ≥ 2, group...

external characterizations. The following equivalences appear in many noncommutative algebra texts such as Anderson & Fuller 1992, §15, Isaacs 1994, §13B...

Boolean expression Boolean ring Boolean function Boolean-valued function Parity function Symmetric Boolean function Conditioned disjunction Field of sets...

gravity spin network black hole thermodynamics Quantum group Hopf algebra Noncommutative quantum field theory See list of string theory topics Matrix model...

Types Algebraic number field Global field Local field Finite field Symmetric function Formally real field Real closed field Applications Galois theory Galois...

analysis or local arithmetic dynamics Noncommutative algebra Noncommutative algebraic geometry a direction in noncommutative geometry studying the geometric...

Dylan G.L. Allegretti, Differential Forms on Noncommutative Spaces. An elementary introduction to noncommutative geometry which uses Hochschild homology to...

functions on three-dimensional space. The Fock spaces then have a natural interpretation as symmetric or anti-symmetric square integrable functions as...

= cos x + i sin x, where cos is the cosine function, i is the imaginary unit and sin is the sine function. x is the argument of the complex number (angle...

the combinatorics of simplicial complexes. F1 has been connected to noncommutative geometry and to a possible proof of the Riemann hypothesis. In 1957...

discrete commutative topological groups, to groups that are compact but noncommutative. The theory is named after Tadao Tannaka and Mark Grigorievich Krein...