We consider a realization of the W1＋∞ algebra and investigate its nn-algebra, which is different from the nn-algebra of Zhang et al. [2016 arXiv：1606.07570v2] It is found that the generators Wm^s with any fixed sup...We consider a realization of the W1＋∞ algebra and investigate its nn-algebra, which is different from the nn-algebra of Zhang et al. [2016 arXiv：1606.07570v2] It is found that the generators Wm^s with any fixed superindex s≥1 yield the null sub-2s-algebra. The nontrivial sub-44-algebra and Virasoro–Witt 3-algebra are presented. Moreover, we extend the generators to the multi-variables case. These generators also yield the W1＋∞ algebra and null nn-algebras.展开更多
We briefly describe the importance of division algebras and Poincaré conjecture in both mathematical and physical scenarios. Mathematically, we argue that using the torsion concept one can combine the formalisms ...We briefly describe the importance of division algebras and Poincaré conjecture in both mathematical and physical scenarios. Mathematically, we argue that using the torsion concept one can combine the formalisms of division algebras and Poincaré conjecture. Physically, we show that both formalisms may be the underlying mathematical tools in special relativity and cosmology. Moreover, we explore the possibility that by using the concept of n-qubit system, such conjecture may allow generalization the Hopf maps.展开更多
We study the Leibniz n-algebra U_(n)(L),whose multiplication is defined via the bracket of a Leibniz algebra L as[x1,…,xn]=[x1,[…,[xn−2,[xn−1,xn]]…]].We show that U_(n)(L)is simple if and only if L is a simple Lie ...We study the Leibniz n-algebra U_(n)(L),whose multiplication is defined via the bracket of a Leibniz algebra L as[x1,…,xn]=[x1,[…,[xn−2,[xn−1,xn]]…]].We show that U_(n)(L)is simple if and only if L is a simple Lie algebra.An analog of Levi's theorem for Leibniz algebras in U_(n)(Lb)is established and it is proven that the Leibniz n-kernel of U_(n)(L)for any semisimple Leibniz algebra L is the n-algebra U_(n)(L).展开更多
We analyze the super n-bracket built from associative operator products.Since the super n-bracket with n even satisfies the so-called generalized super Jacobi identity,we deal with the n odd case and give the generali...We analyze the super n-bracket built from associative operator products.Since the super n-bracket with n even satisfies the so-called generalized super Jacobi identity,we deal with the n odd case and give the generalized super Bremner identity.For the infinite conserved operators in the supersymmetric Landau problem,we derive the super W_(1+∞) n-algebra which satisfies the generalized super Jacobi and Bremner identities for the n even and odd cases,respectively.Moreover the super W_(1+∞) sub-2n-algebra is also given.展开更多
In this paper we show that for an n-Filippov algebra g, the tensor power g ^n-1 is endowed with a structure of anti-symmetric co-representation over the Leibniz algebra g ^n-1. This co-representation is used to define...In this paper we show that for an n-Filippov algebra g, the tensor power g ^n-1 is endowed with a structure of anti-symmetric co-representation over the Leibniz algebra g ^n-1. This co-representation is used to define some relative theories for Leibniz n-algebras with n 〉 2 and obtain exact sequences relating them. As a result, we construct a spectral sequence for the Leibniz homology of Filippov algebras.展开更多
We present the(co)sine n-algebra which is indexed by the d-dimensional integer lattice.Due to the associative operators,this generalized(co)sine n-algebra is the higher order Lie algebra for the n even case.The partic...We present the(co)sine n-algebra which is indexed by the d-dimensional integer lattice.Due to the associative operators,this generalized(co)sine n-algebra is the higher order Lie algebra for the n even case.The particular cases are the d-dimensional lattice sine 3 and cosine 5-algebras with the special parameter values.We find that the corresponding d-dimensional lattice sine 3 and cosine 5-algebras are the Nambu 3-algebra and higher order Lie algebra,respectively.The limiting case of the d-dimensional lattice(co)sine n-algebra is also discussed.Moreover we construct the super sine n-algebra,which is the super higher order Lie algebra for the n even case.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11375119 and 11475116
文摘We consider a realization of the W1＋∞ algebra and investigate its nn-algebra, which is different from the nn-algebra of Zhang et al. [2016 arXiv：1606.07570v2] It is found that the generators Wm^s with any fixed superindex s≥1 yield the null sub-2s-algebra. The nontrivial sub-44-algebra and Virasoro–Witt 3-algebra are presented. Moreover, we extend the generators to the multi-variables case. These generators also yield the W1＋∞ algebra and null nn-algebras.
文摘We briefly describe the importance of division algebras and Poincaré conjecture in both mathematical and physical scenarios. Mathematically, we argue that using the torsion concept one can combine the formalisms of division algebras and Poincaré conjecture. Physically, we show that both formalisms may be the underlying mathematical tools in special relativity and cosmology. Moreover, we explore the possibility that by using the concept of n-qubit system, such conjecture may allow generalization the Hopf maps.
基金The first author was supported by the National Science Foundation(grant number 1658672),USA.
文摘We study the Leibniz n-algebra U_(n)(L),whose multiplication is defined via the bracket of a Leibniz algebra L as[x1,…,xn]=[x1,[…,[xn−2,[xn−1,xn]]…]].We show that U_(n)(L)is simple if and only if L is a simple Lie algebra.An analog of Levi's theorem for Leibniz algebras in U_(n)(Lb)is established and it is proven that the Leibniz n-kernel of U_(n)(L)for any semisimple Leibniz algebra L is the n-algebra U_(n)(L).
基金Supported by National Natural Science Foundation of China under Grant Nos.11375119,11475116,and 11547101
文摘We analyze the super n-bracket built from associative operator products.Since the super n-bracket with n even satisfies the so-called generalized super Jacobi identity,we deal with the n odd case and give the generalized super Bremner identity.For the infinite conserved operators in the supersymmetric Landau problem,we derive the super W_(1+∞) n-algebra which satisfies the generalized super Jacobi and Bremner identities for the n even and odd cases,respectively.Moreover the super W_(1+∞) sub-2n-algebra is also given.
文摘In this paper we show that for an n-Filippov algebra g, the tensor power g ^n-1 is endowed with a structure of anti-symmetric co-representation over the Leibniz algebra g ^n-1. This co-representation is used to define some relative theories for Leibniz n-algebras with n 〉 2 and obtain exact sequences relating them. As a result, we construct a spectral sequence for the Leibniz homology of Filippov algebras.
基金Supported by National Natural Science Foundation of China under Grant Nos.11375119 and 11475116
文摘We present the(co)sine n-algebra which is indexed by the d-dimensional integer lattice.Due to the associative operators,this generalized(co)sine n-algebra is the higher order Lie algebra for the n even case.The particular cases are the d-dimensional lattice sine 3 and cosine 5-algebras with the special parameter values.We find that the corresponding d-dimensional lattice sine 3 and cosine 5-algebras are the Nambu 3-algebra and higher order Lie algebra,respectively.The limiting case of the d-dimensional lattice(co)sine n-algebra is also discussed.Moreover we construct the super sine n-algebra,which is the super higher order Lie algebra for the n even case.
