Access the full text.
Sign up today, get an introductory month for just $19.
M. Scheunert, W. Nahm, V. Rittenberg (1976)
Classification of all simple graded Lie algebras whose Lie algebra is reductive. II. Construction of the exceptional algebrasJournal of Mathematical Physics, 17
M. Blau, J. Figueroa-O’Farrill, C. Hull, G. Papadopoulos (2001)
A new maximally supersymmetric background of IIB superstring theoryJournal of High Energy Physics, 2002
Christian Bär (1998)
ON HARMONIC SPINORS, 29
Mckenzie Wang (1989)
Parallel spinors and parallel formsAnnals of Global Analysis and Geometry, 7
José Figueroa-O'Farrill (2000)
Breaking the -wavesClassical and Quantum Gravity, 17
U. Bruzzo, V. Pestov (1999)
On the structure of DeWitt supermanifoldsJournal of Geometry and Physics, 30
A. Rogers (1986)
Graded manifolds, supermanifolds and infinite-dimensional Grassmann algebrasCommunications in Mathematical Physics, 105
S. Sternberg, Universiṭat Tel-Aviv, Aḳademyah le-madaʿim (1984)
Differential geometric methods in mathematical physics
F. Klinker (2002)
The spinor bundle of Riemannian productsarXiv: Differential Geometry
J. Figueroa-O’Farrill, G. Papadopoulos (2001)
Homogeneous fluxes, branes and a maximally supersymmetric solution of M-theoryJournal of High Energy Physics, 2001
M. Waldrop (1983)
Supersymmetry and supergravity.Science, 220 4596
R. D'Auria, S. Ferrara, M. Lled'o, V. Varadarajan (2000)
Spinor Algebras
M. Scheunert, W. Nahm, V. Rittenberg (1976)
Classification of all simple graded Lie algebras whose Lie algebra is reductive. IJournal of Mathematical Physics, 17
Yi-hong Gao, G. Tian (2000)
Instantons and the monopole-like equations in eight dimensionsJournal of High Energy Physics, 2000
B. Kostant (1977)
Graded manifolds, graded Lie theory, and prequantizationLecture Notes in Mathematics, 570
(2000)
Pseudo-Riemannian metrics with parallel spinor fields and vanishing Ricci tensor. In Global analysis and harmonic analysis (Marseille-Luminy, 1999), volume 4 of Sémin
A. Rogers (1980)
A Global Theory of SupermanifoldsJournal of Mathematical Physics, 21
R. Haag, J. Łopuszański, M. Sohnius (1975)
All possible generators of supersymmetries of the S-matrixNuclear Physics, 88
L. Bergery, A. Ikemakhen (1997)
Sur l'holonomie des variétés pseudo-riemanniennes de signature (n, n)Bulletin de la Société Mathématique de France, 125
J. Michelson (2002)
A pp-wave with 26 superchargesClassical and Quantum Gravity, 19
I. Bena, R. Roiban (2002)
Supergravity pp-wave solutions with 28 and 24 superchargesPhysical Review D, 67
(2003)
Supersymmetric Killing Structures
M. Rothstein (1986)
The axioms of supermanifolds and a new structure arising from themTransactions of the American Mathematical Society, 297
(1997)
Ikemakhen. Sur l’holonomie des variétés pseudo-Riemanniennes de signature (n, n). (On the holonomy of pseudo-Riemannian manifolds with signature
J. Figueroa-O'Farrill (1999)
On the supersymmetries of anti de Sitter vacuaarXiv: High Energy Physics - Theory
Helga Baum, I. Kath (1998)
Parallel Spinors and Holonomy Groups on Pseudo-Riemannian Spin ManifoldsAnnals of Global Analysis and Geometry, 17
(1989)
Michelsohn. Spin geometry, volume 38 of Princeton Mathematical Series
D. Alekseevsky, V. Cort'es (1995)
Classification of N-(Super)-Extended Poincaré Algebras and Bilinear Invariants of the Spinor Representation of Spin (p,q)Communications in Mathematical Physics, 183
J. Wess, B. Zumino (1974)
Supergauge Transformations in Four-DimensionsNuclear Physics, 70
K. Habermann (1990)
The twistor equation on Riemannian manifoldsJournal of Geometry and Physics, 7
M. Blau, J. Figueroa-O’Farrill, C. Hull, G. Papadopoulos (2002)
Penrose limits and maximal supersymmetryClassical and Quantum Gravity, 19
D. Leites (1980)
Introduction to the Theory of SupermanifoldsRussian Mathematical Surveys, 35
R. Bryant (2000)
Pseudo-Reimannian metrics with parallel spinor fields and vanishing Ricci tensor, 4
S. Coleman, J. Mandula (1967)
All Possible Symmetries of the S MatrixPhysical Review, 159
J. Scherk (1978)
Extended Supersymmetry and Extended Supergravity Theories, 44
P. Nath, R. Arnowitt (1980)
Supergravity geometry in superspaceNuclear Physics, 165
Marjorie Batchelor (1979)
The structure of supermanifoldsTransactions of the American Mathematical Society, 253
Helga Baum, T. Friedrich, R. Grunewald, I. Kath (1991)
Twistors and killing spinors on riemannian manifolds
R. Arnowitt, P. Nath (1978)
Superspace formulation of supergravityPhysics Letters B, 78
D. Alekseevsky, V. Cortés, C. Devchand, U. Semmelmann (1997)
Killing spinors are killing vector fields in Riemannian supergeometryJournal of Geometry and Physics, 26
In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo-) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the one hand and spinor fields on the other hand as equivalent geometric objects. This is the starting point of our definition of supersymmetric Killing structures. The latter combines subspaces of vector fields and spinor fields, provided they fulfill certain field equations. This naturally leads to a superalgebra which extends the supersymmetry algebra to the case of non-flat reduced space. We examine in detail the additional terms which enter into this structure and we give a lot of examples.
Communications in Mathematical Physics – Springer Journals
Published: Feb 4, 2005
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get an introductory month for just $19.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.