Get Actions and Invariants of Algebraic Groups PDF

By Walter Ferrer Santos, Alvaro Rittatore

ISBN-10: 082475896X

ISBN-13: 9780824758967

ISBN-10: 1420030795

ISBN-13: 9781420030792

This self-contained advent to geometric invariant thought hyperlinks the idea of affine algebraic teams to Mumford's thought. The authors, professors of arithmetic at Universidad de los angeles República, Uruguay, make the most the perspective of Hopf algebra concept and the speculation of comodules to simplify a few of the correct formulation and proofs. Early chapters evaluation necessities in commutative algebra, algebraic geometry, and the speculation of semisimple Lie algebras. insurance then progresses from Jordan decomposition via homogeneous areas and quotients. bankruptcy workouts, and a thesaurus, notations, and effects are incorporated.

Show description

Read or Download Actions and Invariants of Algebraic Groups PDF

Similar group theory books

Get A first course in noncommutative ring theory PDF

Via aiming the extent of writing on the beginner instead of the gourmand and via stressing the position of examples and motivation, the writer has produced a textual content that's compatible for a one-semester graduate path or for self-study.

Naive Lie Theory - download pdf or read online

During this new textbook, acclaimed writer John Stillwell offers a lucid creation to Lie conception appropriate for junior and senior point undergraduates. so as to accomplish that, he specializes in the so-called "classical groups'' that trap the symmetries of genuine, advanced, and quaternion areas. those symmetry teams might be represented through matrices, which permits them to be studied through easy tools from calculus and linear algebra.

Differentiable Manifolds: A Theoretical Physics Approach by Gerardo F. Torres del Castillo PDF

This textbook explores the idea at the back of differentiable manifolds and investigates a variety of physics purposes alongside the way in which. easy strategies, resembling differentiable manifolds, differentiable mappings, tangent vectors, vector fields, and differential kinds, are in brief brought within the first 3 chapters.

New PDF release: Subgroups of Teichmuller modular groups

Teichmuller modular teams, sometimes called mapping classification teams of surfaces, function a gathering floor for a number of branches of arithmetic, together with low-dimensional topology, the idea of Teichmuller areas, team conception, and, extra lately, mathematical physics. the current paintings focuses normally at the group-theoretic houses of those teams and their subgroups.

Additional resources for Actions and Invariants of Algebraic Groups

Sample text

43. Let X be an algebraic k–variety and assume that Y ⊂ X is a closed subset endowed with the induced topology. 42, Y is said to be a closed subvariety of X, or simply a subvariety. 44. 37 and makes of Y a closed subvariety of X. See Exercise 31. 45. Let X, Y, Z be algebraic varieties, and let f : X → Z, g : Y → Z be morphisms. We define the fibered product of X and Y over Z as a triple (X ×Z Y, pX , pY ) where X ×Z Y is an algebraic variety and 40 1. ALGEBRAIC GEOMETRY pX : X ×Z Y → X, pY : X ×Z Y → Y are morphisms of varieties such that f ◦pX = g ◦pY , and satisfying the following universal property: For an arbitrary triple (W, q1 , q2 ) with W an algebraic variety and q1 : W → X and q2 : W → Y morphisms such that f ◦q1 = g ◦q2 , there exists a unique morphism h : W → X ×Z Y such that q1 = pX ◦h and q2 = pY ◦h.

10), we have that X = V(f1 , . . , fm ). Next we reverse the above construction and associate to an arbitrary subset of An an ideal in the polynomial ring k[X1 , . . , Xn ]. 3. Let X ⊂ An be a arbitrary subset. Call I(X) = f ∈ k[X1 , . . , Xn ] : f |X = 0 ⊂ k[X1 , . . , Xn ] . Notice that I(X) is an ideal of k[X1 , . . , Xn ]. Below we list — and leave as an exercise for the reader to prove — the basic properties of the maps I and V. See Exercise 5. 4. Consider an algebraically closed field k and the maps V and I defined above.

Fn ∈ k[X], g1 , . . ,gn = (x, y) ∈ X × Y : fi (x)gi (y) = 0 . ,gn is a basis for the topology of X × Y . 23 that (X × Y )P fi ⊗gi is isomorphic to the affine variety Spm k[X] ⊗ k[Y ] P fi ⊗gi . ,gn . 25. Let X be an affine algebraic variety. Then the diagonal map ∆ : X → X × X, ∆(x) = (x, x) is a morphism of affine varieties. Moreover, ∆(X) is closed in X × X. 34 1. ALGEBRAIC GEOMETRY Proof: The composition of a regular function α = fi ⊗gi : X ×X → k with ∆ yields the function α ◦ ∆ = fi gi : X → k.

Download PDF sample

Actions and Invariants of Algebraic Groups by Walter Ferrer Santos, Alvaro Rittatore

by Edward

Rated 4.69 of 5 – based on 8 votes