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13. William Stein's Ph.D. thesis
- modular.fas.harvard.edu
- Explicit approaches to modular abelian varieties.
-        I investigate the Birch and Swinnerton-Dyer conjecture, which ties together the constellation of invariants attached to an abelian variety. I attempt to verify this conjecture for certain specific modular abelian varieties of dimension greater than one. ...
- I give an integrated package for computing, in many cases, the following invariants of a modular abelian variety: the modular degree, the rational part of the special value of the L-function, the order of the component group at primes of multiplicative reduction, the period lattice, upper and lower bounds on the torsion subgroup, and the real measure. ...
14. PlanetMath: abelian group
- planetmath.org
- abelian group .
- If for any we have , we say that the group is abelian. ...
- Abelian groups hold several interesting properties.
- Theorem 1 If defined by is a homomorphism, then is abelian. ... Left-mutiplying by and right-multiplying by we are led to and thus the group is abelian. QED Theorem 2 Any subgroup of an abelian group is normal. ... Let be a subgroup of the abelian group. ... QED Theorem 3 Quotient groups of abelian groups are also abelian. ... Since is abelian, is normal and we can get the quotient group whose elements are the equivalence classes for if. ...
- "abelian group" is owned by drini. ...
- See Also: group, subgroup, Klein 4-group, commutative semigroup, locally cyclic group, abelian groups of order , fundamental theorem of finitely generated abelian groups, nonabelian group, commutative Other names: .
- commutative group, abelian, commutative.
- group, abelian, commutative, quotient.
- This is version 12 of abelian group, born on 2003-10-15, modified 2003-10-26. ...
- 20Kxx (Abelian groups).
15. TCS - Research - Publications - Minimum Sum and Difference Covers of Abelian Groups
- www.tcs.hut.fi
- TCS / Research / Publications / Minimum Sum and Difference Covers of Abelian Groups .
- Minimum Sum and Difference Covers of Abelian Groups.
- Minimum sum and difference covers of Abelian groups. ...
16. Polarizations on abelian varieties and self-dual ell-adic representations of inertia groups, by A. Silverberg, Yu. G. Zarhin
- www.math.uiuc.edu
- Polarizations on abelian varieties and self-dual ell-adic representations of inertia groups, by A. ...
- We apply these results to construct, for every odd prime \ell, isogeny classes of abelian varieties all of whose polarizations have degree divisible by \ell. ...
17. STATIONARY AXIALLY SYMMETRIC NON-ABELIAN ROTATING COSMIC STRINGS
- ejournals.wspc.com.sg
- STATIONARY AXIALLY SYMMETRIC NON-ABELIAN ROTATING COSMIC STRINGS.
- It is conjectured that the singular behavior of the metric components at finite distance of the core is related to the gravitational instability found in the self-gravitating flat-space non-Abelian monopole, the Einstein–Skyrme model and Einstein–Yang–Mills–Higgs model.
18. Notes on the non-Abelian BFFT embedding, Schrödinger quantization and the anomaly of the nonlinear sigma model
- www.sbf1.if.usp.br
- Notes on the non-Abelian BFFT embedding, Schrödinger quantization and the anomaly of the nonlinear sigma model.
- We embed the nonlinear sigma model in a non-Abelian gauge theory. ...
- O(N) nonlinear sigma model: non-Abelian .
19. ABELIAN VARIETIES
- turing.wins.uva.nl
- ABELIAN VARIETIES.
- We are preparing a textbook about abelian varieties. ...
- Chapter 2: Line bundles and divisors on abelian varieties .
- Chapter 6: The Picard scheme of an abelian variety .
20. Homological Algebra, Its Non-Abelian and Categorical Topics: Applications to Homotopy Theory, K-Theory, Algebraic Geometry and Galois Theory
- www.crdf.org
- Homological Algebra, Its Non-Abelian and Categorical Topics: Applications to Homotopy Theory, K-Theory, Algebraic Geometry and Galois Theory .
- New descriptions of non-abelian homology groups in terms of derived functors were given. Sufficient conditions were established for non-abelian homology of groups to be finite, finitely generated, p-groups and torsion groups. ...
- Brown and Loday's exact sequence about the relationship of Whitehead's gamma functor with non-abelian tensor product and exterior product of groups was extended for precrossed modules. ...
21. Abelian group - Wikipedia, the free encyclopedia
- en2.wikipedia.org
- Abelian group.
- In mathematics, an abelian group, also called a commutative group, is a group (G, *) such that a * b = b * a for all a and b in G. Abelian groups are named after Niels Henrik Abel.
- 1 Notation 2 Examples 3 Multiplication table 4 Properties 5 Finite abelian groups 6 Relation to other mathematical topics 7 A note on the typography .
- There are two main notational conventions for abelian groups -- additive and multiplicative.
- Every cyclic group G is abelian, because if x, y are in G, then xy = aman = am + n = an + m = anam = yx. ...
- The real numbers form an abelian group under addition, as do the non-zero real numbers under multiplication. Every commutative ring gives rise to two abelian groups in the same fashion -- the additive group of all elements, and the multiplicative group of invertible elements, or units.
- Any subgroup of an abelian group is normal, and hence factor groups can be formed at will. Subgroups, factor groups, products and direct sums of abelian groups are again abelian.
- To verify that a certain finite group is indeed abelian, a table (matrix) can be drawn up in the similar fashion to a multiplication table, where, if the group is G = {g1 = e, g2,. ... The group is abelian if and only if this table is symmetric about the main diagonal (i. ...
- This is true since if the group is abelian, then gi ⋅ gj = gj ⋅ gi. ...
- If n is a natural number and x is an element of an abelian group G, then nx can be defined as x + x +. ... In fact, the modules over Z can be identified with the abelian groups.
- Theorems about abelian groups (i. ... A typical example is the classification of finitely generated abelian groups.
22. hep-th/9511038 New Results in Topological Field Theory and Abelian Gauge Theory
- arxiv.org
- From: Thompson George view email Date: Mon, 6 Nov 1995 17:26:36 +0100 (MET) (46kb) New Results in Topological Field Theory and Abelian Gauge Theory.
23. Non-abelian Gauge Fields
- www-thphys.physics.ox.ac.uk
- Non-abelian Gauge Fields .
- The aim of the course is to provide an introduction into modern theory of strong interactions - Quantum Chromodynamics (QCD) and into some general aspects of non-Abelian gauge theories in general. ...
- The lectures will assume that students have a decent knowledge of the basic quantum field theory course (attending the ``Topological Aspects of QM and QFT'' and "Abelian gauge fields" courses, which start one month earlier, is a big plus). ...
- Asymptotic freedom in one loop approximation, difference between nonabelian and abelian gauge fields. ...
24. Broue's Abelian Defect Group Conjecture
- www.maths.bris.ac.uk
- Broué's Abelian Defect Group Conjecture.
- What is Broué's Abelian Defect Group Conjecture? .
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