### Electronic Research Archive

2021, Issue 4: 2771-2789. doi: 10.3934/era.2021013

# Graded post-Lie algebra structures and homogeneous Rota-Baxter operators on the Schrödinger-Virasoro algebra

• Received: 01 July 2020 Revised: 01 November 2020 Published: 22 February 2021
• Primary: 16W99, 05C05; Secondary: 08A50

• In this paper, we characterize the graded post-Lie algebra structures on the Schrödinger-Virasoro Lie algebra. Furthermore, as an application, we obtain the all homogeneous Rota-Baxter operator of weight $1$ on the Schrödinger-Virasoro Lie algebra.

Citation: Pengliang Xu, Xiaomin Tang. Graded post-Lie algebra structures and homogeneous Rota-Baxter operators on the Schrödinger-Virasoro algebra[J]. Electronic Research Archive, 2021, 29(4): 2771-2789. doi: 10.3934/era.2021013

### Related Papers:

• In this paper, we characterize the graded post-Lie algebra structures on the Schrödinger-Virasoro Lie algebra. Furthermore, as an application, we obtain the all homogeneous Rota-Baxter operator of weight $1$ on the Schrödinger-Virasoro Lie algebra.

 [1] Nonabelian generalized Lax pairs, the classical Yang-Baxter equation and PostLie algebras. Commun. Math. Phys. (2010) 297: 553-596. [2] An analytic problem whose solution follows from a simple algebraic identity. Pacific J. Math. (1960) 10: 731-742. [3] Left-symmetric algebras, or pre-Lie algebras in geometry and physics. Cent. Eur. J. Math. (2006) 4: 323-357. [4] Affine actions on Lie groups and post-Lie algebra structures. Linear Algebra Appl. (2012) 437: 1250-1263. [5] Commutative post-Lie algebra structures on Lie algebras. J. Algebra (2016) 467: 183-201. [6] Rota-Baxter operators on Witt and Virasoro algebras. J. Geom. Phys. (2016) 108: 1-20. [7] (2012) An Introduction to Rota-Baxter Algebra.Somerville: International Press. [8] Generalized operator Yang-Baxter equations, integrable ODES and nonassociative algebras. J. Nonlinear Math. Phys. (2000) 7: 184-197. [9] J. Han, J. Li and Y. Su, Lie bialgebra structures on the Schrödinger-Virasoro Lie algebras, J. Math. Phys., 50 (2009), 083504, 12 pp. [10] Schrödinger invariance and stringly anisotropic critical systems. J. Stat. Phys. (1994) 75: 1023-1061. [11] Biderivations and commutative post-Lie algebra structure on Schrödinger-Virasoro Lie algebras. Bull. Iranian Math. Soc. (2019) 45: 1743-1754. [12] On post-Lie algebras, Lie-Butcher series and moving frames. Found. Comput. Math. (2013) 13: 583-613. [13] Post-Lie algebra structures on the Lie algebra SL (2, $\mathbb{C}$). Electron. J. Linear Algebra (2012) 23: 180-197. [14] Y. Pei and C. Bai, Novikov algebras and Schrödinger-Virasoro Lie algebras, J. Phys., 44 (2011), 045201, 18 pp. doi: 10.1088/1751-8113/44/4/045201 [15] The Schrödinger-Virasoro Lie group and algebra: Representation theory and cohomological study. Ann. Henri Poincaré (2006) 7: 1477-1529. [16] G.-C. Rota, Baxter algebras and combinatorial identities I, Bull. Amer. Math. Soc., 75 (1969), 325–329. doi: 10.1090/S0002-9904-1969-12158-0 [17] G.-C. Rota, Baxter operators, an introduction, in "Gian-Carlo Rota on combinatorics, introductory papers and commentaries", Joesph PS Kung, Editor, J., (1995), 504–512. [18] Post-Lie algebra structures on the Witt algebra. Bull. Malays. Math. Sci. Soc. (2019) 42: 3427-3451. [19] Rota-Baxter operators on $4$-dimensional complex simple associative algebras. Appl. Math. Comput. (2014) 229: 173-186. [20] Graded post-Lie algebra structures, Rota-Baxter operators and Yang-Baxter equations on the W-algebra $W(2, 2)$. Bull. Korean Math. Soc. (2018) 55: 1727-1748. [21] On vertex algrbra representations of the Schrödinger-Virasoro Lie algebra. Nuclear Phys. B (2009) 823: 320-371. [22] Homology of generalized partition posets. J. Pure. Appl. Algebra (2007) 208: 699-725. [23] Weak quasi-symmetric functions, Rota-Baxter algebras and Hopf algebras. Adv. Math. (2019) 344: 1-34.
###### 通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

1.604 0.8

Article outline

Tables(2)

• On This Site