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Jun
21
asked Compact resolvent VS certain boundedness condition
Jun
13
awarded  Supporter
Jun
8
answered Riemann tensor on a sphere
Jun
7
revised 8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries
added 99 characters in body
Jun
7
revised 8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries
deleted 2 characters in body
Jun
7
revised 8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries
added 1026 characters in body
Jun
7
revised 8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries
added 8 characters in body
Jun
7
awarded  Editor
Jun
7
revised 8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries
edited body
Jun
7
asked 8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries
Jun
6
accepted #(cardinality of irreps Lie algebras) > #(irreps of ssociative algebras). Proof?
Jun
6
comment #(cardinality of irreps Lie algebras) > #(irreps of ssociative algebras). Proof?
Since $A\cong\oplus_{i=0}^{N}M_{n_i}(\mathbb{C})$ for any fininte dimensional $*$-algebra $A$, and any matrix algebra direct summand has a unique irrep, to wit $\mathbf{n}=\mathbb{C}^n$ acted on by the left, I get an "obvious" representation for $A$ in the sum $V:=\oplus_i^N \mathbb{n}_{i}$. It seems to me pretty canonical-but, as I told you, I am not sure if that is the term I should use. The point is that I cannot do the same for semisimple Lie algebras, for their classification is quite more complicated, can I?Sorry to ask again, but could you shed some light on the bijection you mentioned?
Jun
5
comment #(cardinality of irreps Lie algebras) > #(irreps of ssociative algebras). Proof?
by canonical I meant, that if I have a $*$-algebra, I can get an canonical representation in the sum of all its irreps. I'm not sure of having used the right word though. Can you shed some light on the bijection you mentioned?
Jun
5
answered Notation for antiderivative
Jun
5
comment #(cardinality of irreps Lie algebras) > #(irreps of ssociative algebras). Proof?
So, given a Lie algebra, you cannot form a canonical representation, can you? (unlike the $*$-algebra case).
Jun
5
awarded  Scholar
Jun
5
awarded  Student
Jun
5
asked #(cardinality of irreps Lie algebras) > #(irreps of ssociative algebras). Proof?