让 L 是块类型在上的谎言代数学与基础 { L ， i|，我 } 并且方括号[L ， i,L,j]=((i+1)-(j+1)) L + ， i+j 。在这份报纸，我们首先构造 L 的正式分发谎言代数学。然后，我们决定它的保角的代数学 B 与[] 基础 { L (w)|} 并且方括号[L (w) L (w)]=(+(+)) L +(w) 。最后，我们给免费中间的系列 B 模块的一个分类。
Based on the analytic property of the symmetric q-exponent e_q(x),a new symmetric q-deformed Kadomtsev-Petviashvili(q-KP for short) hierarchy associated with the symmetric q-derivative operator α_q is constructed.Furthermore,the symmetric q-CKP hierarchy and symmetric q-BKP hierarchy are defined.The authors also investigate the additional symmetries of the symmetric q-KP hierarchy.
Let A = F [x, y] be the polynomial algebra on two variables x, y over an algebraically closed field F of characteristic zero. Under the Poisson bracket, A is equipped with a natural Lie algebra structure. It is proven that the maximal good subspace of A* induced from the multiplication of the associative commutative algebra A coincides with the maximal good subspace of A* induced from the Poisson bracket of the Poisson Lie algebra A. Based on this, structures of dual Lie bialgebras of the Poisson type are investigated. As by-products,five classes of new infinite-dimensional Lie algebras are obtained.
In this paper, we study the structure theory of a class of not-finitely graded Lie algebras related to generalized Heisenberg–Virasoro algebras. In particular, the derivation algebras, the automorphism groups and the second cohomology groups of these Lie algebras are determined.
