- the same
commutative diagrams.): 46
Similar bialgebras are
related by
bialgebra homomorphisms. A
bialgebra homomorphism is a
linear map that is both an...
-
implies that, in practice, one
studies only
classes of
bialgebras that are
cohomologous to a Lie
bialgebra on a coboundary. They are also
called Poisson-Hopf...
-
between simply connected Poisson–Lie
groups and finite-dimensional Lie
bialgebras.
Thanks to
Drinfeld theorem, any Poisson–Lie
group G {\displaystyle G}...
- *f_{m})^{*}(x)=f_{1}^{*}(x)+\cdots +f_{m}^{*}(x).} Let (X, Δ, ∇, ε, η) be a
bialgebra with
comultiplication Δ,
multiplication ∇, unit η, and
counit ε. The convolution...
- . The
exterior algebra (as well as the
symmetric algebra)
inherits a
bialgebra structure, and, indeed, a Hopf
algebra structure, from the
tensor algebra...
-
concept of a
cofree coalgebra, and a more
complicated one,
which yields a
bialgebra, and can be
extended by
giving an
antipode to
create a Hopf
algebra structure...
- 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...
-
Objects like this are
called bialgebras, and in fact most of the
important coalgebras considered in
practice are
bialgebras.
Examples of
coalgebras include...
-
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...
