Lecture 8 - Universal Enveloping Algebras and Related Concepts, II
... Graded Ideals. If U is graded and I is an ideal, then I isLcalled a graded ideal provided that if x ∈ I, then also each π i (x) ∈ I. That is, I = i I ∩ U i . If U is graded and I is a graded ideal, then U/I is graded. Inherited Filtrations. If π : A → B is a surjection of algebras and A is filtered ...
... Graded Ideals. If U is graded and I is an ideal, then I isLcalled a graded ideal provided that if x ∈ I, then also each π i (x) ∈ I. That is, I = i I ∩ U i . If U is graded and I is a graded ideal, then U/I is graded. Inherited Filtrations. If π : A → B is a surjection of algebras and A is filtered ...
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... 3. N (xy) = N (x)N (y). Examples. All examples considered below have ground ring the reals R. • KD(R, −1) = C, the complex numbers. • KD(C, −1) = H, the quaternions. • KD(H, −1) = O, the octonions. • KD(O, −1) = S, which are called the sedenions, an algebra of dimension 16 over R. Remarks. 1. Starti ...
... 3. N (xy) = N (x)N (y). Examples. All examples considered below have ground ring the reals R. • KD(R, −1) = C, the complex numbers. • KD(C, −1) = H, the quaternions. • KD(H, −1) = O, the octonions. • KD(O, −1) = S, which are called the sedenions, an algebra of dimension 16 over R. Remarks. 1. Starti ...
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... Unique Number: 56055 Meeting Time: Monday–Wednesday–Friday, 10:00 am to 11:00 am Room: RLM 9.166 Text: Abstract Algebra, 3rd edition by Dummit and Foote, published by Wiley Brief Course Description: This course is a continuation of the fall graduate algebra course M380C, currently taught by David He ...
... Unique Number: 56055 Meeting Time: Monday–Wednesday–Friday, 10:00 am to 11:00 am Room: RLM 9.166 Text: Abstract Algebra, 3rd edition by Dummit and Foote, published by Wiley Brief Course Description: This course is a continuation of the fall graduate algebra course M380C, currently taught by David He ...
