- In mathematics, a
bialgebra over a
field K is a
vector space over K
which is both a
unital ****ociative
algebra and a
counital co****ociative coalgebra...
- does not make it a
bialgebra, but does lead to the
concept of a
cofree coalgebra, and a more
complicated one,
which yields a
bialgebra, and can be extended...
- In mathematics, a Lie
bialgebra is the Lie-theoretic case of a
bialgebra: it is a set with a Lie
algebra and a Lie
coalgebra structure which are compatible...
- quasi-
bialgebras are a
generalization of
bialgebras: they were
first defined by the
Ukrainian mathematician Vladimir Drinfeld in 1990. A quasi-
bialgebra differs...
- co****ociative) coalgebra, with
these structures'
compatibility making it a
bialgebra, and that
moreover is
equipped with an
antihomomorphism satisfying a certain...
- . The
exterior algebra (as well as the
symmetric algebra)
inherits a
bialgebra structure, and, indeed, a Hopf
algebra structure, from the
tensor algebra...
-
satisfying these conditions. This is the
motivation for the
definition of a
bialgebra,
where Δ is
called the
comultiplication and ε is
called the counit. In...
-
operators Vector space Linear algebra Algebra-like
Algebra ****ociative Non-****ociative
Composition algebra Lie
algebra Graded Bialgebra Hopf
algebra v t e...
-
operators Vector space Linear algebra Algebra-like
Algebra ****ociative Non-****ociative
Composition algebra Lie
algebra Graded Bialgebra Hopf
algebra v t e...
- manifold. The
infinitesimal counterpart of a Poisson–Lie
group is a Lie
bialgebra, in
analogy to Lie
algebras as the
infinitesimal counterparts of Lie groups...
