"양자 다이로그 항등식 (quantum dilogarithm identities)"의 두 판 사이의 차이
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Pythagoras0 (토론 | 기여) |
Pythagoras0 (토론 | 기여) |
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| 9번째 줄: | 9번째 줄: | ||
* Faddeev-Kashaev 양자 [[5항 관계식 (5-term relation) |5항 관계식 (5-term relation)]] | * Faddeev-Kashaev 양자 [[5항 관계식 (5-term relation) |5항 관계식 (5-term relation)]] | ||
:<math>(v;q)_{\infty}(u;q)_{\infty}=(u;q)_{\infty}(-vu;q)_{\infty}(v;q)_{\infty}</math><br> | :<math>(v;q)_{\infty}(u;q)_{\infty}=(u;q)_{\infty}(-vu;q)_{\infty}(v;q)_{\infty}</math><br> | ||
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| + | ==리뷰논문, 에세이, 강의노트== | ||
| + | * [http://www.math.jussieu.fr/%7Ekeller/publ/QuiverMutQuantDilogHandout.pdf Quiver mutations and quantum dilogarithm identities], presentation, Isle of Skye, June 27, 2011 | ||
| + | * [http://www.birs.ca/events/2010/5-day-workshops/10w5069/videos Quantum dilogarithm identities from quiver mutations], video of a talk given at Banff, September 9, 2010. | ||
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| 15번째 줄: | 23번째 줄: | ||
* Bytsko, Andrei, and Alexander Volkov. 2013. “Tetrahedron Equation and Cyclic Quantum Dilogarithm Identities.” arXiv:1304.1641 (April 5). http://arxiv.org/abs/1304.1641. | * Bytsko, Andrei, and Alexander Volkov. 2013. “Tetrahedron Equation and Cyclic Quantum Dilogarithm Identities.” arXiv:1304.1641 (April 5). http://arxiv.org/abs/1304.1641. | ||
* Faddeev, L. D. 2012. “Volkov’s Pentagon for the Modular Quantum Dilogarithm.” arXiv:1201.6464 (January 31). http://arxiv.org/abs/1201.6464. | * Faddeev, L. D. 2012. “Volkov’s Pentagon for the Modular Quantum Dilogarithm.” arXiv:1201.6464 (January 31). http://arxiv.org/abs/1201.6464. | ||
| + | * Kashaev, Rinat M., and Tomoki Nakanishi. 2011. “Classical and Quantum Dilogarithm Identities.” arXiv:1104.4630 (April 24). doi:10.3842/SIGMA.2011.102. http://arxiv.org/abs/1104.4630. | ||
| + | * Keller, Bernhard. 2011. “On Cluster Theory and Quantum Dilogarithm Identities.” arXiv:1102.4148 (February 21). http://arxiv.org/abs/1102.4148. | ||
* [http://dx.doi.org/10.1142/S0217732394000447 Quantum Dilogarithm] L.D.<em style="line-height: 2em;">Fadeev</em> and R.M.<em style="line-height: 2em;">Kashaev</em>, Mod. Phys. Lett. A. 9 (1994) p.427–434 [http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&s4=&s5=&s6=&s7=Quantum%20Dilogarithm&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=52&mx-pid=1264393 MR1264393(95i:11150)] | * [http://dx.doi.org/10.1142/S0217732394000447 Quantum Dilogarithm] L.D.<em style="line-height: 2em;">Fadeev</em> and R.M.<em style="line-height: 2em;">Kashaev</em>, Mod. Phys. Lett. A. 9 (1994) p.427–434 [http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&s4=&s5=&s6=&s7=Quantum%20Dilogarithm&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq&r=52&mx-pid=1264393 MR1264393(95i:11150)] | ||
2013년 5월 30일 (목) 02:49 판
바일 대수(Weyl algebra)와 양자 다이로그 항등식
- 양자 바일 대수와 양자평면 참조
- \(\mathbb{C}[q,q^{-1}]\) 위에서 u,v 로 생성되는 대수, \(uv=qvu\) 를 만족시킴
- q-이항계수 (가우스 다항식) 에서 양자평면이라는 이름으로 사용됨
- q-이항계수 (가우스 다항식) 에서 양자평면이라는 이름으로 사용됨
- Schützenberger 항등식
\[(u;q)_{\infty}(v;q)_{\infty}=(u+v;q)_{\infty}\]
- Faddeev-Volkov 항등식
\[(v;q)_{\infty}(u;q)_{\infty}=(u+v-vu;q)_{\infty}\]
- Faddeev-Kashaev 양자 5항 관계식 (5-term relation)
\[(v;q)_{\infty}(u;q)_{\infty}=(u;q)_{\infty}(-vu;q)_{\infty}(v;q)_{\infty}\]
리뷰논문, 에세이, 강의노트
- Quiver mutations and quantum dilogarithm identities, presentation, Isle of Skye, June 27, 2011
- Quantum dilogarithm identities from quiver mutations, video of a talk given at Banff, September 9, 2010.
관련논문
- Fu, Changjian, and Liangang Peng. 2013. “Quantum Dilogarithm Identities and Cyclic Quivers.” arXiv:1305.5395 (May 23). http://arxiv.org/abs/1305.5395.
- Bytsko, Andrei, and Alexander Volkov. 2013. “Tetrahedron Equation and Cyclic Quantum Dilogarithm Identities.” arXiv:1304.1641 (April 5). http://arxiv.org/abs/1304.1641.
- Faddeev, L. D. 2012. “Volkov’s Pentagon for the Modular Quantum Dilogarithm.” arXiv:1201.6464 (January 31). http://arxiv.org/abs/1201.6464.
- Kashaev, Rinat M., and Tomoki Nakanishi. 2011. “Classical and Quantum Dilogarithm Identities.” arXiv:1104.4630 (April 24). doi:10.3842/SIGMA.2011.102. http://arxiv.org/abs/1104.4630.
- Keller, Bernhard. 2011. “On Cluster Theory and Quantum Dilogarithm Identities.” arXiv:1102.4148 (February 21). http://arxiv.org/abs/1102.4148.
- Quantum Dilogarithm L.D.Fadeev and R.M.Kashaev, Mod. Phys. Lett. A. 9 (1994) p.427–434 MR1264393(95i:11150)