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 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.
