- correspondence, the
commutative finite-dimensional
algebras correspond to the
cocommutative finite-dimensional coalgebras. So in the finite-dimensional case, the...
- finite-dimensional case[clarification needed], or if H is
commutative or
cocommutative (or more
generally quasitriangular). In general, S is an antihomomorphism...
-
certain 4-dimensional
quotient of it that is
neither commutative nor
cocommutative. The
following infinite dimensional Hopf
algebra was
introduced by Sweedler...
-
algebra of a Lie algebra, both of
which are also
cocommutative Hopf algebras. In
general cocommutative Hopf
algebras behave very much like groups. For...
- y]=xy-yx} (graded
commutator if C is graded). If A is a
connected graded cocommutative Hopf
algebra over a
field of
characteristic zero, then the Milnor–Moore...
-
positive selfadjoint graded Hopf
algebra that is both
commutative and
cocommutative. The
study of
symmetric functions is
based on that of
symmetric polynomials...
-
algebraic topology. The
theorem states:
given a connected, graded,
cocommutative Hopf
algebra A over a
field of
characteristic zero with dim A n <...
- is in some
sense as far as
possible from
being either commutative or
cocommutative. It was
introduced by
Malvenuto &
Reutenauer (1995) and
studied by Poirier...
-
Laurent polynomial ring can be
endowed with a
structure of a commutative,
cocommutative Hopf algebra.
Jones polynomial Weisstein, Eric W. "Laurent Polynomial"...
- on how the
boundary components are
grouped –
which is
commutative or
cocommutative,
while the map ****ociated with a disk
gives a
counit (trace) or unit...
