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Jun 7 |
comment |
8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries I thought it was a very soft-question for people familiar with K-theory, but what you say sounds very reasonable. I'll reedit the question. |
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Jun 7 |
revised |
8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries added 8 characters in body |
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Jun 7 |
comment |
8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries Thank you for the reference. I restated the question. Now, Connes doesn't quite explain why the dimension he introduces for spectral triples has a K-theoretical meaning. It is not obvious for non-K-theorists, at least. |
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Jun 7 |
awarded | Editor |
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Jun 7 |
revised |
8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries edited body |
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Jun 7 |
asked | 8 periodicity: Clifford clock- Bott periodicity - KO-dimension in noncommutative geometries |
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Jun 6 |
accepted | #(cardinality of irreps Lie algebras) > #(irreps of ssociative algebras). Proof? |
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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? |
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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? |
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Jun 5 |
answered | Notation for antiderivative |
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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). |
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Jun 5 |
awarded | Scholar |
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Jun 5 |
awarded | Student |
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Jun 5 |
asked | #(cardinality of irreps Lie algebras) > #(irreps of ssociative algebras). Proof? |
