In algebra, the Malvenuto–Poirier–Reutenauer Hopf algebra of permutations or MPR Hopf algebra is a Hopf algebra with a basis of all elements of all the...

In mathematics, a Hopf algebra, named after Heinz Hopf, is a structure that is simultaneously a (unital associative) algebra and a (counital coassociative)...

a shuffle algebra is a Hopf algebra with a basis corresponding to words on some set, whose product is given by the shuffle product X ⧢ Y of two words...

cocommutative graded Hopf algebra. It has the Hopf algebra of symmetric functions as a quotient, and is a subalgebra of the Hopf algebra of permutations, and is the...

p} , the Steenrod algebra A p {\displaystyle A_{p}} is the graded Hopf algebra over the field F p {\displaystyle \mathbb {F} _{p}} of order p {\displaystyle...

selfadjoint graded Hopf algebra that is both commutative and cocommutative. The study of symmetric functions is based on that of symmetric polynomials...

defined as a permutation on this set containing 1 or 2 rising sequences. The permutations with 1 rising sequence are the identity permutations. As a special...

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

coefficients from integers to the rational numbers. To any group ring or Hopf algebra is associated its representation ring or "Green ring". The representation...

known for her work on the Hopf algebra of permutations Michelle Manes, American mathematician interested in number theory, algebraic geometry, and dynamical...

algebra forming a Hopf algebra. The representation theory of the symmetric group is a particular case of the representation theory of finite groups, for...

mathematician, one of the namesakes of the Malvenuto–Poirier–Reutenauer Hopf algebra of permutations. She is an associate professor of mathematics at Sapienza...

Representation theory of Hopf algebras General Associative property, Associator Heap (mathematics) Magma (algebra) Loop (algebra), Quasigroup Nonassociative...

Automorphism of a Lie algebra Frobenius integrability theorem (the integrability being the same as being a Lie subalgebra) Gelfand–Fuks cohomology Hopf algebra Index...

In abstract algebra, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with...

the group algebra of the symmetric group whose coefficients are the same for permutations with the same peaks. (Here a peak of a permutation σ on {1,2...

theorem to hold). Just as for Lie algebras, the universal enveloping algebra of the Lie superalgebra can be given a Hopf algebra structure. Lie superalgebras...

terms of partial permutations. It also has a denotational semantics in which formulas are interpreted by modules over some specific Hopf algebras. By extension...

dual vector space. The Hopf algebras associated to groups have a commutative algebra structure, and so general Hopf algebras are known as quantum groups...

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants...

of this is the peak algebra. The Malvenuto–Reutenauer algebra is a Hopf algebra based on permutations that relates the rings of symmetric functions,...

Baxter permutations are related to Hopf algebras, planar graphs, and tilings. Baxter introduced Baxter permutations while studying the fixed points of commuting...

certain permutations of the roots. At first, Galois's ideas were rejected by his contemporaries, and published only posthumously. More general permutation groups...

representation Principal series representation Borel–Weil–Bott theorem Algebra representation Representation theory of Hopf algebras Quiver (mathematics)...

to other categories in abstract algebra: associative algebras, rings, Lie algebras, Lie superalgebras, Hopf algebras to name some. Representations or...

was a completely new point of view. Noether's suggestion that topology be studied algebraically was adopted immediately by Hopf, Alexandrov, and others,...

and in this way, G is the group Hopf algebra F1[G]. Toric varieties determine F1‑varieties. In some descriptions of F1‑geometry the converse is also...

Birkhoff, G. (1999). Algebra. AMS Chelsea. ISBN 0-8218-1646-2. Aguiar, M.; Mahajan, S. (2010). Monoidal functors, species and Hopf algebras. CRM Monograph Series...

Artin–Tits group Braided monoidal category Braided vector space Braided Hopf algebra Knot theory Non-commutative cryptography Spherical braid group Weisstein...

fields of one-dimensional domains and their completions. Mathematics portal Toric geometry Torus Torus based cryptography Hopf algebra Milne. "Algebraic Groups:...