Timeline for Rep of Non-Commutative Monoids
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29, 2014 at 14:28 | comment | added | Benjamin Steinberg | Look at the books of Putcha and Renner on algebraic monoids. The group of units of an irreducible linear algebraic monoid with 0 is reductive iff the monoid is von Neumann regular. The functions are a direct sum if irreducible one-dim reps iff the monoid is an affine toric variety in which case it is commutative. | |
| Mar 29, 2014 at 13:04 | comment | added | Giulio | Could you suggest me any reference with a language closer to algebraic geometry/ standard hopf algebras and rep theory please | |
| Mar 29, 2014 at 13:03 | comment | added | Giulio | Do you also show that it is reductive? I mean: do you show that the algebra of functions over M split as a direct sum of one dim irr repp?? | |
| Mar 29, 2014 at 12:47 | comment | added | Benjamin Steinberg | My paper is about finite things. Your situation is quite different because you are infinite dimensional. In all situations that I am used to having a unique idempotent is the same as being a group because in a usual linear algebraic monoid the group if units is open and it's complement is an algebraic semigroup and hence has idempotents if nonempty. | |
| Mar 29, 2014 at 9:26 | vote | accept | Giulio | ||
| Mar 28, 2014 at 17:52 | history | edited | Benjamin Steinberg | CC BY-SA 3.0 |
Added link; added 59 characters in body; added 1 characters in body
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| Mar 28, 2014 at 17:42 | history | answered | Benjamin Steinberg | CC BY-SA 3.0 |