- ****ociativity of
algebra multiplication (called the co****ociativity of the
comultiplication); the
second diagram is the dual of the one
expressing the existence...
- Hopf
algebra is
particularly nice,
since the
existence of
compatible comultiplication, counit, and
antipode allows for the
construction of
tensor products...
-
structures are made
compatible with a few more axioms. Specifically, the
comultiplication and the
counit are both
unital algebra homomorphisms, or equivalently...
-
axiom of the counit. A
bialgebra defines both multiplication, and
comultiplication, and
requires them to be compatible.
Multiplication is
given by an...
- the
lattice Primitive element (coalgebra), an
element X on
which the
comultiplication Δ has the
value Δ(X) = X⊗1 + 1⊗X
Primitive element (free group), an...
- {id} \otimes \varepsilon )\circ \rho =\mathrm {id} } ,
where Δ is the
comultiplication for C, and ε is the counit. Note that in the
second rule we have identified...
- Λ2(V),
where the
first map is the
comultiplication along the
first coordinate. The
other map is a
comultiplication Λ4(V) → Λ2(V) ⊗ Λ2(V). For a partition...
-
examples of *-algebras (with the
additional structure of a
compatible comultiplication); the most
familiar example being: The
group Hopf algebra: a group...
- is
dense in C;
There exists a C*-algebra
homomorphism called the
comultiplication Δ: C → C ⊗ C (where C ⊗ C is the C*-algebra
tensor product - the completion...
-
space is a Lie algebra,
whereas the
comultiplication is a 1-cocycle, so that the
multiplication and
comultiplication are compatible. The
cocycle condition...
