Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2023, Cilt: 33 Sayı: 33, 247 - 269, 09.01.2023

Vsevolod Gubarev Roman Kozlov

https://doi.org/10.24330/ieja.1218727

Öz

Anahtar Kelimeler

Lie conformal algebra Rota---Baxter operator conformal classical Yang---Baxter equation

Kaynakça

  • M. Aguiar, Pre-Poisson algebras, Lett. Math. Phys., 54(4) (2000), 263-277.
  • A. D'Andrea and V. G. Kac, Structure theory of finite conformal algebras, Selecta Math., 4(3) (1998), 377-418.
  • C. Bai, O. Bellier, L. Guo and X. Ni, Splitting of operations, Manin products, and Rota---Baxter operators, Int. Math. Res. Not., 3 (2013), 485-524.
  • B. Bakalov, A. D'Andrea and V. G. Kac, Theory of finite pseudoalgebras, Adv. Math., 162(1) (2001), 1-140.
  • G. Baxter, An analytic problem whose solution follows from a simple algebraic identity, Pacific J. Math., 10 (1960), 731-742.
  • A. A. Belavin, V. G. Drinfel'd, Solutions of the classical Yang---Baxter equation for simple Lie algebras, Funktsional. Anal. i Prilozhen., 16(3) (1982), 1-29.
  • A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nuclear Phys. B, 241(2) (1984), 333-380.
  • P. Benito, V. Gubarev and A. Pozhidaev, Rota---Baxter operators on quadratic algebras, Mediterr. J. Math., 15(5) (2018), 189 (23 pp).
  • R. E. Borcherds, Vertex algebras, Kac–Moody algebras, and the monster, Proc. Nat. Acad. Sci. U.S.A., 83(10) (1986), 3068-3071.
  • C. Boyallian and J. I. Liberati, On pseudo-bialgebras, J. Algebra, 372 (2012), 1-34.
  • D. Burde and V. Gubarev, Rota---Baxter operators and post-Lie algebra structures on semisimple Lie algebras, Comm. Algebra, 47(5) (2019), 2280-2296.
  • E. Frenkel and D. Ben-Zvi, Vertex Algebras and Algebraic Curves, Mathematical Surveys and Monographs, 88. American Mathematical Society, Providence, RI, 2001.
  • M. Goncharov and V. Gubarev, Double Lie algebras of nonzero weight, Adv. Math., 409 (2022), 108680 (30 pp).
  • M. E. Goncharov and P. S. Kolesnikov, Simple finite-dimensional double algebras, J. Algebra, 500 (2018), 425-438.
  • V. Gubarev and P. Kolesnikov, Embedding of dendriform algebras into Rota---Baxter algebras, Cent. Eur. J. Math., 11(2) (2013), 226-245.
  • V. Gubarev and R. Kozlov, Conformal Yang---Baxter equation on $\Cur(\sl_2(\mathbb{C}))$, arXiv:2209.12431, (20~pp).
  • L. Guo, An Introduction to Rota---Baxter Algebra, Surveys of Modern Mathematics, 4. International Press, Somerville, MA; Higher Education Press, Beijing, 2012.
  • Y. Hong and C. Bai, Conformal classical Yang-Baxter equation, $S$-equation and $\mathcal{O}$-operators, Lett. Math. Phys., 110(5) (2019), 885-909.
  • V. G. Kac, Vertex Algebras for Beginners, University Lecture Series, 10. American Mathematical Society, Providence, RI, 1997.
  • P. Kolesnikov, Homogeneous averaging operators on simple finite conformal Lie algebras, J. Math. Phys., 56(7) (2015), 071702 (10 pp).
  • E. I. Konovalova, Double Lie Algebras, PhD thesis, Samara State University, 2009, 189 pp. (in Russian).
  • J. Lepowsky and H. Li, Introduction to Vertex Operator Algebras and Their Representations, Progress in Mathematics, 227. Birkhäuser Boston, Inc., Boston, MA, 2004.
  • J. I. Liberati, conformal bialgebras, J. Algebra, 319(6) (2008), 2295-2318.
  • L. Liu and S. Wang, Rota---Baxter $H$-operators and pre-Lie $H$-pseudoalgebras over a~cocommutative Hopf algebra $H$, Linear Multilinear Algebra, 68(11) (2020), 2170-2184.
  • J. Liu, S. Zhou and L. Yuan, Conformal $r$-matrix-Nijenhuis structures, symplectic-Nijenhuis structures and $\mathcal{O}N$-structures, J. Math. Phys., 63(10) (2022), 101701 (22 pp).
  • Y. Pan, Q. Liu, C. Bai and L. Guo, PostLie algebra structures on the Lie algebra $\mathrm{sl}(2,\mathbb{C})$, Electron. J. Linear Algebra, 23 (2012), 180-197.
  • L. Yuan, $\mathcal{O}$-operators and Nijenhius operators of associative conformal algebras, J. Algebra, 609 (2022), 245-291.
  • J. Zhao, L. Chen and B. Sun, Representations and cohomology of Rota---Baxter Lie conformal algebras, preprint (researchgate), 2021, 18 pp.

Rota---Baxter operators on $Cur(sl_2(\mathbb{C}))$

Yıl 2023, Cilt: 33 Sayı: 33, 247 - 269, 09.01.2023

Vsevolod Gubarev Roman Kozlov

https://doi.org/10.24330/ieja.1218727

Öz

We classify all Rota---Baxter operators on the simple Lie conformal algebra $\Cur(\sl_2(\mathbb{C}))$ and clarify which of them arise from the solutions to the conformal classical Yang---Baxter equation due to the connection discovered by Y. Hong and C. Bai in 2020.

Anahtar Kelimeler

Lie conformal algebra Rota---Baxter operator conformal classical Yang---Baxter equation

Kaynakça

  • M. Aguiar, Pre-Poisson algebras, Lett. Math. Phys., 54(4) (2000), 263-277.
  • A. D'Andrea and V. G. Kac, Structure theory of finite conformal algebras, Selecta Math., 4(3) (1998), 377-418.
  • C. Bai, O. Bellier, L. Guo and X. Ni, Splitting of operations, Manin products, and Rota---Baxter operators, Int. Math. Res. Not., 3 (2013), 485-524.
  • B. Bakalov, A. D'Andrea and V. G. Kac, Theory of finite pseudoalgebras, Adv. Math., 162(1) (2001), 1-140.
  • G. Baxter, An analytic problem whose solution follows from a simple algebraic identity, Pacific J. Math., 10 (1960), 731-742.
  • A. A. Belavin, V. G. Drinfel'd, Solutions of the classical Yang---Baxter equation for simple Lie algebras, Funktsional. Anal. i Prilozhen., 16(3) (1982), 1-29.
  • A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, Infinite conformal symmetry in two-dimensional quantum field theory, Nuclear Phys. B, 241(2) (1984), 333-380.
  • P. Benito, V. Gubarev and A. Pozhidaev, Rota---Baxter operators on quadratic algebras, Mediterr. J. Math., 15(5) (2018), 189 (23 pp).
  • R. E. Borcherds, Vertex algebras, Kac–Moody algebras, and the monster, Proc. Nat. Acad. Sci. U.S.A., 83(10) (1986), 3068-3071.
  • C. Boyallian and J. I. Liberati, On pseudo-bialgebras, J. Algebra, 372 (2012), 1-34.
  • D. Burde and V. Gubarev, Rota---Baxter operators and post-Lie algebra structures on semisimple Lie algebras, Comm. Algebra, 47(5) (2019), 2280-2296.
  • E. Frenkel and D. Ben-Zvi, Vertex Algebras and Algebraic Curves, Mathematical Surveys and Monographs, 88. American Mathematical Society, Providence, RI, 2001.
  • M. Goncharov and V. Gubarev, Double Lie algebras of nonzero weight, Adv. Math., 409 (2022), 108680 (30 pp).
  • M. E. Goncharov and P. S. Kolesnikov, Simple finite-dimensional double algebras, J. Algebra, 500 (2018), 425-438.
  • V. Gubarev and P. Kolesnikov, Embedding of dendriform algebras into Rota---Baxter algebras, Cent. Eur. J. Math., 11(2) (2013), 226-245.
  • V. Gubarev and R. Kozlov, Conformal Yang---Baxter equation on $\Cur(\sl_2(\mathbb{C}))$, arXiv:2209.12431, (20~pp).
  • L. Guo, An Introduction to Rota---Baxter Algebra, Surveys of Modern Mathematics, 4. International Press, Somerville, MA; Higher Education Press, Beijing, 2012.
  • Y. Hong and C. Bai, Conformal classical Yang-Baxter equation, $S$-equation and $\mathcal{O}$-operators, Lett. Math. Phys., 110(5) (2019), 885-909.
  • V. G. Kac, Vertex Algebras for Beginners, University Lecture Series, 10. American Mathematical Society, Providence, RI, 1997.
  • P. Kolesnikov, Homogeneous averaging operators on simple finite conformal Lie algebras, J. Math. Phys., 56(7) (2015), 071702 (10 pp).
  • E. I. Konovalova, Double Lie Algebras, PhD thesis, Samara State University, 2009, 189 pp. (in Russian).
  • J. Lepowsky and H. Li, Introduction to Vertex Operator Algebras and Their Representations, Progress in Mathematics, 227. Birkhäuser Boston, Inc., Boston, MA, 2004.
  • J. I. Liberati, conformal bialgebras, J. Algebra, 319(6) (2008), 2295-2318.
  • L. Liu and S. Wang, Rota---Baxter $H$-operators and pre-Lie $H$-pseudoalgebras over a~cocommutative Hopf algebra $H$, Linear Multilinear Algebra, 68(11) (2020), 2170-2184.
  • J. Liu, S. Zhou and L. Yuan, Conformal $r$-matrix-Nijenhuis structures, symplectic-Nijenhuis structures and $\mathcal{O}N$-structures, J. Math. Phys., 63(10) (2022), 101701 (22 pp).
  • Y. Pan, Q. Liu, C. Bai and L. Guo, PostLie algebra structures on the Lie algebra $\mathrm{sl}(2,\mathbb{C})$, Electron. J. Linear Algebra, 23 (2012), 180-197.
  • L. Yuan, $\mathcal{O}$-operators and Nijenhius operators of associative conformal algebras, J. Algebra, 609 (2022), 245-291.
  • J. Zhao, L. Chen and B. Sun, Representations and cohomology of Rota---Baxter Lie conformal algebras, preprint (researchgate), 2021, 18 pp.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Vsevolod Gubarev Bu kişi benim

Roman Kozlov Bu kişi benim

Yayımlanma Tarihi 9 Ocak 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 33 Sayı: 33

Kaynak Göster

APA Gubarev, V., & Kozlov, R. (2023). Rota---Baxter operators on $Cur(sl_2(\mathbb{C}))$. International Electronic Journal of Algebra, 33(33), 247-269. https://doi.org/10.24330/ieja.1218727
AMA Gubarev V, Kozlov R. Rota---Baxter operators on $Cur(sl_2(\mathbb{C}))$. IEJA. Ocak 2023;33(33):247-269. doi:10.24330/ieja.1218727
Chicago Gubarev, Vsevolod, ve Roman Kozlov. “Rota---Baxter Operators on $Cur(sl_2(\mathbb{C}))$”. International Electronic Journal of Algebra 33, sy. 33 (Ocak 2023): 247-69. https://doi.org/10.24330/ieja.1218727.
EndNote Gubarev V, Kozlov R (01 Ocak 2023) Rota---Baxter operators on $Cur(sl_2(\mathbb{C}) $. International Electronic Journal of Algebra 33 33 247–269.
IEEE V. Gubarev ve R. Kozlov, “Rota---Baxter operators on $Cur(sl_2(\mathbb{C}))$”, IEJA, c. 33, sy. 33, ss. 247–269, 2023, doi: 10.24330/ieja.1218727.
ISNAD Gubarev, Vsevolod - Kozlov, Roman. “Rota---Baxter Operators on $Cur(sl_2(\mathbb{C}))$”. International Electronic Journal of Algebra 33/33 (Ocak 2023), 247-269. https://doi.org/10.24330/ieja.1218727.
JAMA Gubarev V, Kozlov R. Rota---Baxter operators on $Cur(sl_2(\mathbb{C}))$. IEJA. 2023;33:247–269.
MLA Gubarev, Vsevolod ve Roman Kozlov. “Rota---Baxter Operators on $Cur(sl_2(\mathbb{C}))$”. International Electronic Journal of Algebra, c. 33, sy. 33, 2023, ss. 247-69, doi:10.24330/ieja.1218727.
Vancouver Gubarev V, Kozlov R. Rota---Baxter operators on $Cur(sl_2(\mathbb{C}))$. IEJA. 2023;33(33):247-69.