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4 results on '"Junna Ni"'

1. Some Results on Zinbiel Algebras and Rota–Baxter Operators

Author

Jizhong Gao, Junna Ni, and Jianhua Yu

Subjects
Zinbiel algebra, commutative associative algebra, Rota–Baxter operator, deviation, Mathematics, QA1-939
Abstract

Rota–Baxter operators (RBOs) play a substantial role in many subfields of mathematics, especially in mathematical physics. In the article, RBOs on Zinbiel algebras (ZAs) and their sub-adjacent algebras are first investigated. Moreover, all the RBOs on two and three-dimensional ZAs are presented. Finally, ZAs are also realized in low dimensions of the RBOs of commutative associative algebras. It was found that not all ZAs can be attained in this way.

Published
2024
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2. Novikov Super-Algebras with Associative Non-Degenerate Super-Symmetric Bilinear Forms

Author

Junna Ni and Zhiqi Chen

Subjects
Pure mathematics, Integrable system, Degenerate energy levels, Statistical and Nonlinear Physics, Bilinear form, Mathematics::Algebraic Topology, Algebra, symbols.namesake, Nilpotent, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Quadratic equation, Mathematics::K-Theory and Homology, symbols, Novikov self-consistency principle, Hamiltonian (quantum mechanics), Mathematical Physics, Associative property, Mathematics
Abstract

Novikov super-algebras are related to quadratic conformal super-algebras which correspond to Hamiltonian pairs and play fundamental role in completely integrable systems. In this paper, we focus on quadratic Novikov super-algebras, which are Novikov super-algebras with associative non-degenerate super-symmetric bilinear forms. We show that quadratic Novikov super-algebras are associative and the associated Lie-super algebras of quadratic Novikov super-algebras are 2-step nilpotent. Moreover, we give some properties on quadratic Novikov super-algebras and classify the associated Lie-super algebras of quadratic Novikov super-algebras up to dimension 7.

Published
2021

3. Super -operators of Jordan superalgebras and super Jordan Yang-Baxter equations

Author

Dongping Hou, Junna Ni, and Yan Wang

Subjects
Algebra, Pure mathematics, Mathematics (miscellaneous), Algebraic structure, Mathematics::Quantum Algebra, Mathematics::Rings and Algebras, Mathematics::Representation Theory, Image (mathematics), Mathematics
Abstract

In this paper, the super Open image in new window-operators of Jordan superalgebras are introduced and the solutions of super Jordan Yang-Baxter equation are discussed by super Open image in new window-operators. Then pre-Jordan superalgebras are studied as the algebraic structure behind the super Open image in new window-operators. Moreover, the relations among Jordan superalgebras, pre-Jordan superalgebras, and dendriform superalgebras are established.

Published
2014

4. Some Notes on Quadratic Lie Triple Systems.

Author

Junna Ni and Jianhua Yu

Subjects
*STEINER systems, *MATHEMATICAL decomposition, *QUADRATIC equations, *MATHEMATICAL research, *MATHEMATICAL analysis
Abstract

In this paper, the decompositions of quadratic Lie triple systems are discussed. Moreover the decomposition theorems of a quadratic Lie triple system into nondegenerate irreducible ideals are established. [ABSTRACT FROM AUTHOR]

Published
2010

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