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Tuynman G.M. — Supermanifolds and Supergroups: Basic Theory
Tuynman G.M. — Supermanifolds and Supergroups: Basic Theory



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Название: Supermanifolds and Supergroups: Basic Theory

Автор: Tuynman G.M.

Аннотация:

Supermanifolds and Supergroups explains the basic ingredients of super manifolds and super Lie groups. It starts with super linear algebra and follows with a treatment of super smooth functions and the basic definition of a super manifold. When discussing the tangent bundle, integration of vector fields is treated as well as the machinery of differential forms. For super Lie groups the standard results are shown, including the construction of a super Lie group for any super Lie algebra. The last chapter is entirely devoted to super connections. The book requires standard undergraduate knowledge on super differential geometry and super Lie groups. Some knowledge of ordinary differential geometry is helpful when reading the text.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 431

Добавлена в каталог: 17.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Strong bundle map      147
Structure, bundle      361
Structure, constants of a Lie algebra      272 273 280 297 328 340
Structure, equations of an $\mathcal{A}$-Lie group      340
Structure, group      145
Subalgebra of a Lie algebra      28 293
Subbundle      160
Subbundle, integrable      243 244 342
Subbundle, involutive      243
Submanifold      130
Submodule      2
Submodule, $\mathfrak{A}$-graded      4 6
Submodule, generated by      6
Submodule, sum of      6
Subspace of an $\mathcal{A}$-vector space      86
Subspace, graded      59 86
Sum of submodules      6
Supplement      15 63
Supplement of a bundle      165
Support of a function      134
Support of a section      159
Symmetric, $\mathfrak{A}$-graded      24
Symplectic geometry      332
Tangent, bundle      204
Tangent, map      212
Tangent, map, generalized      225 257
Tangent, to a subbundle      244
Tensor product      18
Tensor product of vector bundles      166
Topology on an $\mathcal{A}$-vector space      93
Topology, DeWitt      93
Topology, second countable      128 245 247
Trace      76
Trace, graded      75 76 80 285
Transition function      145
Transitive action      267
TRANSPOSE      71
Transpose of a morphism      13
Transpose, graded      71
Transposition operator      13
Trilinear map      8
Trivial bundle      147 223 224
Trivial vector bundle      158 223 224
Trivializing atlas      145
Trivializing chart      144
Trivializing sections, set of      160
Type p k-form      396
Typical fiber      145
Vector bundle      156
Vector field      209
Vector field, Euler      261
Vector field, fundamental      299
Vector field, integrable      228
Vector field, invariant      315
Vector field, left/right-invariant      270
Vertical subbundle      342
Vertical tangent vectors      342
Wave      228
Wedge product      26
Wedge product for vector bundle valued forms      336 386
Wedge product, symbol      26
Whitney sum      164
Without odd dimensions      106 136
Yang — Baxter equation      23
Zero section      158
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