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Journals and Conferences
In this paper, the different operator forms of classical Yang-Baxter equation are given in the tensor expression through a unified algebraic method. It is closely related to left-symmetric algebras which play an important role in many fields in mathematics and mathematical physics. By studying the relations between left-symmetric algebras and classical… (More)
We introduce a notion of left-symmetric bialgebra which is an analogue of the notion of Lie bialgebra. We prove that a left-symmetric bialgebra is equivalent to a symplectic Lie algebra with a decomposition into a direct sum of the underlying vector spaces of two Lagrangian subalgebras. The latter is called a parakähler Lie algebra or a phase space of a Lie… (More)
In this paper, some left-symmetric algebras are constructed from linear functions. They include a kind of simple left-symmetric algebras and some examples appearing in mathematical physics. Their complete classification is also given, which shows that they can be regarded as generalization of certain 2-dimensional left-symmetric algebras.
We investigate multiple qubit Pauli groups and the quantum states/rays arising from their maximal bases. Remarkably, the real rays are carried by a Barnes-Wall lattice BWn (n = 2m). We focus on the smallest subsets of rays allowing a state proof of the BellKochen-Specker theorem (BKS). BKS theorem rules out realistic non-contextual theories by resorting to… (More)
We introduce the concept of an extended O-operator that generalizes the wellknown concept of a Rota-Baxter operator. We study the associative products coming from these operators and establish the relationship between extended O-operators and the associative Yang-Baxter equation, extended associative Yang-Baxter equation and generalized Yang-Baxter equation.
Related Articles Representations of some quantum tori Lie subalgebras J. Math. Phys. 54, 032302 (2013) The Poincaré algebra in rank 3 simple Lie algebras J. Math. Phys. 54, 023508 (2013) Relativistic Chasles' theorem and the conjugacy classes of the inhomogeneous Lorentz group J. Math. Phys. 54, 022501 (2013) Localization in abelian Chern-Simons theory J.… (More)
A non-abelian phase space, or a phase space of a Lie algebra is a generalization of the usual (abelian) phase space of a vector space. It corresponds to a parakähler structure in geometry. Its structure can be interpreted in terms of left-symmetric algebras. In particular, a solution of an algebraic equation in a left-symmetric algebra which is an analogue… (More)