Wed Feb 7 and Fri Feb 9
Friday:
"Bilinearity" is only a good notion for commutative rings, and is then closely related to tensor products.
How to show a tensor product is big or small.
If R,S are k-algebras, and A,B are modules over them, then A @k B is a module over R @k S.
In the R=S case, sometimes there are interesting "comultiplications" R -> R @k R.
Def. Symmetric algebra, group algebra, monoid algebra.
The co-commutative comultiplication on a monoid algebra.
"Bilinearity" is only a good notion for commutative rings, and is then closely related to tensor products.
How to show a tensor product is big or small.
If R,S are k-algebras, and A,B are modules over them, then A @k B is a module over R @k S.
In the R=S case, sometimes there are interesting "comultiplications" R -> R @k R.
Def. Symmetric algebra, group algebra, monoid algebra.
The co-commutative comultiplication on a monoid algebra.
posted by Allen Knutson @ 11:40 AM
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