![arXiv:math/0009100v1 [math.DG] 10 Sep 2000](http://s1.studyres.com/store/data/000152175_1-8b3fe2b443d17ea217220901b35aa35c-300x300.png)
arXiv:math/0009100v1 [math.DG] 10 Sep 2000
... Note that in a topological groupoid G for each a ∈ G(x, y) right translation Ra : Gx → Gy , b 7→ ba and left translation La : Gy → Gx , b 7→ ab are homeomorphisms. A groupoid G in which each star Gx has a topology such that for a ∈ G(x, y) the right translation Ra : Gx → Gy , b 7→ ba (and hence the ...
... Note that in a topological groupoid G for each a ∈ G(x, y) right translation Ra : Gx → Gy , b 7→ ba and left translation La : Gy → Gx , b 7→ ab are homeomorphisms. A groupoid G in which each star Gx has a topology such that for a ∈ G(x, y) the right translation Ra : Gx → Gy , b 7→ ba (and hence the ...
On linearly ordered H-closed topological semilattices
... This order is called natural. An element e of a semilattice E is called minimal (maximal) if f ≤ e (e ≤ f ) implies f = e for f ∈ E. For elements e and f of a semilattice E we write e < f if e ≤ f and e = f . A semilattice E is said to be linearly ordered or a chain if the natural order on E is lin ...
... This order is called natural. An element e of a semilattice E is called minimal (maximal) if f ≤ e (e ≤ f ) implies f = e for f ∈ E. For elements e and f of a semilattice E we write e < f if e ≤ f and e = f . A semilattice E is said to be linearly ordered or a chain if the natural order on E is lin ...
Groupoid C*-algebras with Hausdorff Spectrum
... Suppose that the maps of H/Hx onto H · x are homeomorphisms for each x ∈ X . The spectrum C ∗ (H n X )∧ is Hausdorff if and only if the map x 7→ Hx is continuous with respect to the Fell topology and X /H is Hausdorff. Note: We can use [Orloff Clark; 07] and [Ramsay; 90] to show that if either X /H ...
... Suppose that the maps of H/Hx onto H · x are homeomorphisms for each x ∈ X . The spectrum C ∗ (H n X )∧ is Hausdorff if and only if the map x 7→ Hx is continuous with respect to the Fell topology and X /H is Hausdorff. Note: We can use [Orloff Clark; 07] and [Ramsay; 90] to show that if either X /H ...
Version of 18.4.08 Chapter 44 Topological groups Measure theory
... measures on locally compact Hausdorff groups, is the fact that they are, up to scalar multiples, unique. This is the content of 442B. We find also that while left and right Haar measures can be different, they are not only direct mirror images of each other (442C) – as is, I suppose, to be expected ...
... measures on locally compact Hausdorff groups, is the fact that they are, up to scalar multiples, unique. This is the content of 442B. We find also that while left and right Haar measures can be different, they are not only direct mirror images of each other (442C) – as is, I suppose, to be expected ...
Pobierz - DML-PL
... that a map which is homotopic to a sufficiently regular one (called essential) has a fixed point, or the equation involving this map admits a solution. However, one should have a convenient tool for deciding whether a given map (or one that a given map can be homotopically deformed to) is essential. ...
... that a map which is homotopic to a sufficiently regular one (called essential) has a fixed point, or the equation involving this map admits a solution. However, one should have a convenient tool for deciding whether a given map (or one that a given map can be homotopically deformed to) is essential. ...
Lecture Notes for Math 614, Fall, 2015
... g generate C[x] over C? This will be the case if and only if x ∈ C[f, g], i.e., if and only if x can be expressed as a polynomial with complex coefficients in f and g. For example, suppose that f = x5 + x3 − x2 + 1 and g = x14 − x7 + x2 + 5. Here it is easy to see that f and g do not generate, becau ...
... g generate C[x] over C? This will be the case if and only if x ∈ C[f, g], i.e., if and only if x can be expressed as a polynomial with complex coefficients in f and g. For example, suppose that f = x5 + x3 − x2 + 1 and g = x14 − x7 + x2 + 5. Here it is easy to see that f and g do not generate, becau ...
Algebraic Number Theory, a Computational Approach
... Basic Commutative Algebra The commutative algebra in this chapter provides a foundation for understanding the more refined number-theoretic structures associated to number fields. First we prove the structure theorem for finitely generated abelian groups. Then we establish the standard properties of ...
... Basic Commutative Algebra The commutative algebra in this chapter provides a foundation for understanding the more refined number-theoretic structures associated to number fields. First we prove the structure theorem for finitely generated abelian groups. Then we establish the standard properties of ...
The Lambda Calculus is Algebraic - Department of Mathematics and
... which the lambda calculus is equivalent to an algebraic theory. The basic observation is that the failure of the ξ-rule is not a deficiency of the lambda calculus itself, nor of combinatory algebras, but rather it is an artifact of the way free variables are interpreted in a model. Under the usual i ...
... which the lambda calculus is equivalent to an algebraic theory. The basic observation is that the failure of the ξ-rule is not a deficiency of the lambda calculus itself, nor of combinatory algebras, but rather it is an artifact of the way free variables are interpreted in a model. Under the usual i ...
The Brauer group of a field - Mathematisch Instituut Leiden
... algebras over a field k are division rings for which a ring isomorphism between the center and k is given and the underlying k-vector space is finite-dimensional, as are the n × nmatrix rings over these division rings for n ∈ Z>0 . The ring of quaternions H, introduced by William Hamilton (1805–1865), ...
... algebras over a field k are division rings for which a ring isomorphism between the center and k is given and the underlying k-vector space is finite-dimensional, as are the n × nmatrix rings over these division rings for n ∈ Z>0 . The ring of quaternions H, introduced by William Hamilton (1805–1865), ...
Algebraic Number Theory, a Computational Approach
... Basic Commutative Algebra The commutative algebra in this chapter provides a foundation for understanding the more refined number-theoretic structures associated to number fields. First we prove the structure theorem for finitely generated abelian groups. Then we establish the standard properties of ...
... Basic Commutative Algebra The commutative algebra in this chapter provides a foundation for understanding the more refined number-theoretic structures associated to number fields. First we prove the structure theorem for finitely generated abelian groups. Then we establish the standard properties of ...
Spectral measures in locally convex algebras
... mappings t h a t can, with respect to their spectral behavior, be properly viewed as generalizations of finite matrices with linear elementary divisors. The theory presented in this paper is intended to show t h a t spectral theory, in the sense presently discussed: is not intrinsically connected wi ...
... mappings t h a t can, with respect to their spectral behavior, be properly viewed as generalizations of finite matrices with linear elementary divisors. The theory presented in this paper is intended to show t h a t spectral theory, in the sense presently discussed: is not intrinsically connected wi ...
Homological algebra
Homological algebra is the branch of mathematics that studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precursor to algebraic topology) and abstract algebra (theory of modules and syzygies) at the end of the 19th century, chiefly by Henri Poincaré and David Hilbert. The development of homological algebra was closely intertwined with the emergence of category theory. By and large, homological algebra is the study of homological functors and the intricate algebraic structures that they entail. One quite useful and ubiquitous concept in mathematics is that of chain complexes, which can be studied both through their homology and cohomology. Homological algebra affords the means to extract information contained in these complexes and present it in the form of homological invariants of rings, modules, topological spaces, and other 'tangible' mathematical objects. A powerful tool for doing this is provided by spectral sequences.From its very origins, homological algebra has played an enormous role in algebraic topology. Its sphere of influence has gradually expanded and presently includes commutative algebra, algebraic geometry, algebraic number theory, representation theory, mathematical physics, operator algebras, complex analysis, and the theory of partial differential equations. K-theory is an independent discipline which draws upon methods of homological algebra, as does the noncommutative geometry of Alain Connes.