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Algebras of Quotients and Crossed Modules for Lie Color Algebras

Author: PeiFeng
Tutor: ZhouJianHua
School: Southeast University
Course: Basic mathematics
Keywords: Lie color algebra Quotient algebra Crossed Modules Semiprime Essentially ideal Homogeneous partial derivation Cohomology
CLC: O153.3
Type: Master's thesis
Year: 2005
Downloads: 43
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Abstract


Classic ring theory by ring ring structure , the quotient algebra of the Lie algebra concept . On this basis , we propose the concept of Lie color algebra quotient algebra and weak quotient algebra , some properties of Lie color algebra is defined as primality , semi- primality and non- degenerative , and primality and semi - primality promotion to Lie color algebra quotient algebra . Use of no non December annihilator ideal Lie color algebra the quotient algebra portrayed proved : L the subalgebra Lie color algebra Q , Q is L quotient algebra if and only if Q ideal absorption in L . By the specific structure of each semiprime Lie color algebra have greatly quotient algebra , and gives a great characterization of the quotient algebra . On the basis of the Lie algebra of the cross - mode concept , this paper presents the Lie color algebra crossed modules . Is defined from the cross - mode starting Lie color algebra given L , P and the order of the P-mold M , consider all M as nuclei , and P is the remainder of nuclear L of the cross mode , defined between these cross die an equivalence relation , resulting cross - mode equivalence class set of CML (P, L; M), proved CML ( P, L ; same M ) and three-dimensional homology group H (P , L ; M ) there is a one-to-one correspondence between zero homogeneous part , which can take advantage of the three-dimensional crossed modules of Lie color algebra cohomology group classification .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Abstract algebra ( Algebra ) > Ring Theory
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