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Yao Ma

Publications and source records attributed to Yao Ma.

189 records · Page 11Linked to original sources
arXiv2014

An Emergent World of Gauge Force and Partons

We illustrate how a completely new world of gauge force emerges from a conventional condensed matter system in a rigorous way. A characteristic energy scale (Mott gap) separates such an exotic universe from the ordinary one that we condensed matter physicists are more familiar with at higher energies. The governing physical law is no longer about individual electrons but concerns fractionalized particles, i.e., partons, as the new collective modes resulted from strong correlation among the electrons. Novel phenomena in this low-energy universe are clearly distinguished from Landau's Fermi liquid described by the perturbative quantum many-body theory.

cond-mat.str-el↗
arXiv2014

On the Deformation of Lie-Yamaguti algebras

The deformation theory of Lie-Yamaguti algebras is developed by choosing a suitable cohomology. The relationship between the deformation and the obstruction of Lie-Yamaguti algebras is obtained.

math.RT↗
arXiv2014

On the cohomology and extensions of $n$-ary multiplicative Hom-Nambu-Lie superalgebras

In this paper, we discuss the representations of $n$-ary multiplicative Hom-Nambu-Lie superalgebras as a generalization of the notion of representations for $n$-ary multiplicative Hom-Nambu-Lie algebras. We also give the cohomology of an $n$-ary multiplicative Hom-Nambu-Lie superalgebra and obtain a relation between extensions of an $n$-ary multiplicative Hom-Nambu-Lie superalgebra $\mathfrak{b}$ by an abelian one $\mathfrak{a}$ and $Z^1(\mathfrak{b}, \mathfrak{a})_{\bar{0}}$. We also introduce the notion of $T^*$-extensions of $n$-ary multiplicative Hom-Nambu-Lie superalgebras and prove that every finite-dimensional nilpotent metric $n$-ary multiplicative Hom-Nambu-Lie superalgebra $(\g,[\cdot,\cdots,\cdot]_{\g},α,\langle ,\rangle_{\g})$ over an algebraically closed field of characteristic not 2 in the case $α$ is a surjection is isometric to a suitable $T^*$-extension.

math.RT↗
arXiv2013

Cohomology and 1-parameter formal deformations of Hom-Lie triple systems

In this paper, we study the cohomology theory of Hom-Lie triple systems generalizing the Yamaguti cohomology theory of Lie triple systems. We introduce the central extension theory for Hom-Lie triple systems and show that there is a one-to-one correspondence between equivalent classes of central extensions of Hom-Lie triple systems and the third cohomology group. We develop the 1-parameter formal deformation theory of Hom-Lie triple systems, and prove that it is governed by the cohomology group.

math.RA↗
arXiv2013

On the cohomology and extensions of first-class $n$-Lie superalgebras

An $n$-Lie superalgebra of parity 0 is called a first-class $n$-Lie superalgebra. In this paper, we give the representation and cohomology for a first-class $n$-Lie superalgebra and obtain a relation between extensions of a first-class $n$-Lie superalgebra $\mathfrak{b}$ by an abelian one $\mathfrak{a}$ and $Z^1(\mathfrak{b}, \mathfrak{a})_{\bar{0}}$. We also introduce the notion of $T^*$-extensions of first-class $n$-Lie superalgebras and prove that every finite-dimensional nilpotent metric first-class $n$-Lie superalgebra $(\g,< ,>_{\g})$ over an algebraically closed field of characteristic not 2 is isometric to a suitable $T^*$-extension.

math.RT↗
arXiv2013

Hom-Nijienhuis operator and $T$*-extension of Hom-Lie Superalgebras

In this paper, we study hom-Lie superalgebras. We give the definition of hom-Nijienhuis operators of regualr hom-Lie superalgebras and show that the deformation generated by a hom-Nijienhuis operator is trivial. Moreover, we introduce the definition of $T^*$-extensions of Hom-Lie superalgebras and show that $T^*$-extensions preserve many properties such as nilpotency, solvability and decomposition in some sense. We also investigate the equivalence of $T^*$-extensions.

math.RA↗
arXiv2013

Systems of quotients of Lie triple systems

In this paper, we introduce the notion of system of quotients of Lie triple systems and investigate some properties which can be lifted from a Lie triple system to its systems of quotients. We relate the notion of Lie triple system of Martindale-like quotients with respect to a filter of ideals and the notion of system of quotients, and prove that the system of quotients of a Lie triple system is equivalent to the algebra of quotients of a Lie algebra in some sense, and these allow us to construct the maximal system of quotients for nondegenerate Lie triple systems.

math.RA↗
arXiv2013

Representations and module-extensions of hom 3-Lie algebras

In this paper, we study the representations and module-extensions of hom 3-Lie algebras. We show that a linear map between hom 3-Lie algebras is a morphism if and only if its graph is a hom 3-Lie subalgebra and show that the derivations of a hom 3-Lie algebra is a Lie algebra. Derivation extension of hom 3-Lie algebras are also studied as an application. Moreover, we introduce the definition of $T_θ$-extensions and $T^{*}_θ$-extensions of hom 3-Lie sub-algebras in terms of modules, provide the necessary and sufficient conditions for $2k$-dimensional metric hom 3-Lie algebra to be isomorphic to a $T^{*}_θ$-extensions.

math.RA↗