"Quantized coordinate ring"의 두 판 사이의 차이
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imported>Pythagoras0 |
imported>Pythagoras0 |
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| 13번째 줄: | 13번째 줄: | ||
* $A_q(\mathfrak{g}):=\{\varphi \in U_q^{*} | \dim U_q \varphi, \dim \varphi U_q <\infty \}$ | * $A_q(\mathfrak{g}):=\{\varphi \in U_q^{*} | \dim U_q \varphi, \dim \varphi U_q <\infty \}$ | ||
* We call $A_q(\mathfrak{g})$ the quantized coordinate ring | * We call $A_q(\mathfrak{g})$ the quantized coordinate ring | ||
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| + | ==related items== | ||
| + | * [[Q-boson algebras]] | ||
2014년 8월 8일 (금) 20:25 판
introduction
- Monoidal categorifications of cluster algebras
- $\mathbb{C}[N]$ is Hopf dual to $U(\mathfrak{n})$ where $\mathfrak{n}=Lie(N)$
- Ringel, Lusztig : Geometric realization of $U_q(\mathfrak{n})$ via constructible sheaves on varieties of $\mathbb{C}Q$-modules
- Lusztig : Geometric realization of $U(n)$ via constructible functions on varieties of $\Lambda$-modules
- Geiss-Leclerc-S : Dualizing Lusztig's construction, get a cluster character
dual of quantized enveloping algebras
- $\mathfrak{g}$ : simple Lie algebra over $\mathbb{C}$
- $U_q:=U_q(\mathfrak{g})$ : quantum enveloping algebra
- $U_q^{*}=\operatorname{Hom}_{\mathbb{Q}(q)}(U_q,\mathbb{Q}(q))$
- $A_q(\mathfrak{g}):=\{\varphi \in U_q^{*} | \dim U_q \varphi, \dim \varphi U_q <\infty \}$
- We call $A_q(\mathfrak{g})$ the quantized coordinate ring