Titlebook: Lectures on Algebraic Quantum Groups; Ken A. Brown,Ken R. Goodearl Textbook 2002 Springer Basel AG 2002 algebra.algebraic group.quantum gr

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Ken A. Brown,Ken R. Goodearlitself one of the most profound questions ever faced by scie.The dark matter problem is one of the most fundamental and profoundly difficult to solve problems in the history of science. Not knowing what makes up most of the known universe goes to the heart of our understanding of the Universe and ou

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Structure and Representation Theory of ,,(g)with , Generic,we proved for .. in Chapter I.4. The role of binomial coefficients in the presentations of these algebras is taken by a q-analogue of binomial coefficients, which we begin by defining. As before, . denotes a nonzero scalar in our base field .

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Polynomial Identity Algebras, say that . satisfies .=.(..,...,..) means .(..,...,..)=0 for all ..,...,.. ∈ .. That . is . means that at least one of the monomials of highest degree in . has coefficient 1; here degree refers to total degree. The . of a PI ring . is the least degree of a monic polynomial identity for .

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Further Quantized Coordinate Rings,Many other quantizations of classical algebras, in addition to the basic examples discussed in the previous chapter, have been constructed. We present a selection here, from those given in terms of generators and relations.

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Bialgebras and Hopf Algebras,As usual, our base field . will remain fixed throughout, and unadorned tensor products ? will mean . Given vector spaces V and W, the . W. V is the linear transformation sending v ?w H w ?v for y E V and . E W.