L-octo-algebra with 8 operations as the Lie algebraic analogue of octo- algebra such that the sum of 8 operations is a Lie algebra is discussed. Any octo- algebra is an L-octo-algebra. The relationships among L-octo-a...L-octo-algebra with 8 operations as the Lie algebraic analogue of octo- algebra such that the sum of 8 operations is a Lie algebra is discussed. Any octo- algebra is an L-octo-algebra. The relationships among L-octo-algebras, L-quadri- algebras, L-dendriform algebras, pre-Lie algebras and Lie algebras are given. The close relationships between L-octo-algebras and some interesting structures like Rota- Baxter operators, classical Yang-Baxter equations and some bilinear forms satisfying certain conditions are given also.展开更多
In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash produc...In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash products, two-sided smash products and two-sided crossed products and prove that they are all associative algebras. Then we show the isomorphic relations of them.展开更多
这份报纸介绍了 L 模糊的潜水艇格子含意代数学的概念并且讨论了它的性质。证明L模糊的潜水艇格子含意代数学的一个家庭的交叉集合是L模糊的潜水艇格子含意代数学，如果并且仅当它的每个切割集合是潜水艇格子含意代数学，一个L模糊的代...这份报纸介绍了 L 模糊的潜水艇格子含意代数学的概念并且讨论了它的性质。证明L模糊的潜水艇格子含意代数学的一个家庭的交叉集合是L模糊的潜水艇格子含意代数学，如果并且仅当它的每个切割集合是潜水艇格子含意代数学，一个L模糊的代用品格子含意代数学设定，这是L模糊的潜水艇格子含意代数学，并且图象和原版在格子含意同形下面L模糊的潜水艇格子含意代数学想象，这两个都是L模糊的潜水艇格子含意代数学。展开更多
引入局部条件并半格 (简记为 L cusl)及其理想完备化等概念 .证明了 :任一代数 L domain的紧元集是 L cusl;任一代数 L domain是其紧元集赋予 Alexandrov拓扑时的 Sober化 ;任一 L cusl的理想完备化是代数 L domain,从而得到了代数 L do...引入局部条件并半格 (简记为 L cusl)及其理想完备化等概念 .证明了 :任一代数 L domain的紧元集是 L cusl;任一代数 L domain是其紧元集赋予 Alexandrov拓扑时的 Sober化 ;任一 L cusl的理想完备化是代数 L domain,从而得到了代数 L domain的表示定理 .还证明了 Scott连续映射为态射的代数 L domain范畴为 L cusl与单调映射作成的范畴的反射子范畴 .展开更多
文摘L-octo-algebra with 8 operations as the Lie algebraic analogue of octo- algebra such that the sum of 8 operations is a Lie algebra is discussed. Any octo- algebra is an L-octo-algebra. The relationships among L-octo-algebras, L-quadri- algebras, L-dendriform algebras, pre-Lie algebras and Lie algebras are given. The close relationships between L-octo-algebras and some interesting structures like Rota- Baxter operators, classical Yang-Baxter equations and some bilinear forms satisfying certain conditions are given also.
基金Foundation item： Supported by the Scientific Research Foundation for Doctoral Scientists of Henan University of Science and Technology（09001303） Supported by the National Natural Science Foundation of China（11101128）
文摘In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash products, two-sided smash products and two-sided crossed products and prove that they are all associative algebras. Then we show the isomorphic relations of them.
文摘这份报纸介绍了 L 模糊的潜水艇格子含意代数学的概念并且讨论了它的性质。证明L模糊的潜水艇格子含意代数学的一个家庭的交叉集合是L模糊的潜水艇格子含意代数学，如果并且仅当它的每个切割集合是潜水艇格子含意代数学，一个L模糊的代用品格子含意代数学设定，这是L模糊的潜水艇格子含意代数学，并且图象和原版在格子含意同形下面L模糊的潜水艇格子含意代数学想象，这两个都是L模糊的潜水艇格子含意代数学。
文摘引入局部条件并半格 (简记为 L cusl)及其理想完备化等概念 .证明了 :任一代数 L domain的紧元集是 L cusl;任一代数 L domain是其紧元集赋予 Alexandrov拓扑时的 Sober化 ;任一 L cusl的理想完备化是代数 L domain,从而得到了代数 L domain的表示定理 .还证明了 Scott连续映射为态射的代数 L domain范畴为 L cusl与单调映射作成的范畴的反射子范畴 .
