The concept of groups with multiple operators can be found in [1] or [2].It's simply called Ω-Group.In this paper,we introduce the concept of -radical in Ω-Groups and discribe (G) and -semisimple (2-Groups. Then...The concept of groups with multiple operators can be found in [1] or [2].It's simply called Ω-Group.In this paper,we introduce the concept of -radical in Ω-Groups and discribe (G) and -semisimple (2-Groups. Then,we expand the results about rings and modules to Ω-Groups.展开更多
Based on the spectral now and the stratification structures of the symplectic group Sp(2n, c) , the Maslov-type index theory and its generalization, the w-index theory parameterized by all ω on the unit circle, for a...Based on the spectral now and the stratification structures of the symplectic group Sp(2n, c) , the Maslov-type index theory and its generalization, the w-index theory parameterized by all ω on the unit circle, for arbitrary paths in Sp(2n, C) are established. Then the Bott-type iteration formula of the Maslov-type indices for iterated paths in Sp(2n, C) is proved, and the mean index for any path in Sp(2n, C) is defined. Also, the relation among various Maslov-type index theories is studied.展开更多
文摘The concept of groups with multiple operators can be found in [1] or [2].It's simply called Ω-Group.In this paper,we introduce the concept of -radical in Ω-Groups and discribe (G) and -semisimple (2-Groups. Then,we expand the results about rings and modules to Ω-Groups.
基金National Natural Science Foundation of China MCSEC of China Qiu Shi Science and Technology Foundation.
文摘Based on the spectral now and the stratification structures of the symplectic group Sp(2n, c) , the Maslov-type index theory and its generalization, the w-index theory parameterized by all ω on the unit circle, for arbitrary paths in Sp(2n, C) are established. Then the Bott-type iteration formula of the Maslov-type indices for iterated paths in Sp(2n, C) is proved, and the mean index for any path in Sp(2n, C) is defined. Also, the relation among various Maslov-type index theories is studied.
