# Introduction to SH Lie algebras for physicists

@article{Lada1993IntroductionTS,
title={Introduction to SH Lie algebras for physicists},
journal={International Journal of Theoretical Physics},
year={1993},
volume={32},
pages={1087-1103}
}
• Published 24 September 1992
• Mathematics
• International Journal of Theoretical Physics
UNC-MATH-92/2originally April 27, 1990, revised September 24, 1992INTRODUCTION TO SH LIE ALGEBRAS FOR PHYSICISTSTom LadaJim StasheffMuch of point particle physics can be described in terms of Lie algebras andtheir representations. Closed string ﬁeld theory, on the other hand, leads to ageneralization of Lie algebra which arose naturally within mathematics in the studyof deformations of algebraic structures [SS]. It also appeared in work on higherspin particles [BBvD]. Representation theoretic…
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## References

SHOWING 1-10 OF 61 REFERENCES
Perturbation Theory in Dierential Homological Algebra II
• Engineering, Physics
• 1989
A multilayer wiring substrate composed of organic dielectric layers with wiring layers disposed therein supports large-scale integrated circuit chips and bonding pads. To prevent damage to the wiring
Cohomology Theory of Lie Groups and Lie Algebras
• Mathematics
• 1948
The present paper lays no claim to deep originality. Its main purpose is to give a systematic treatment of the methods by which topological questions concerning compact Lie groups may be reduced to
Constrained Poisson algebras and strong homotopy representations
A Poisson algebra is a commutative associative algebra A with an (anticommutative) bracket { , } which is a derivation with respect to the commutative product: {f,gh} = {f,g}h + /{g^h}. Constraints
Geometric derivation of string field theory from first principles: Closed strings and modular invariance.
• Kaku
• Physics
Physical review. D, Particles and fields
• 1988
Following the analogy with general relativity and Yang-Mills theory, a new infinite-dimensional local gauge group is defined, called the unified string group, which uniquely specifies the connection fields, the curvature tensor, the measure and tensor calculus, and finally the action itself.
Modular-invariant closed-string field theory.
• Physics
Physical review. D, Particles and fields
• 1988
This work proves the existence of the tetrahedron graph, which is generated by gauge fixing the geometric theory's local gauge group, the unified string group, and is the exact counterpart of the instantaneous four-fermion Coulomb term found in QED.
TheC*-algebra of bosonic strings
We give a rigorous definition of Witten'sC*-string-algebra. To this end we present a new construction ofC*-algebras associated to special geometric situations (Kähler foliations) and generalize this
Covariant string field theory. II.
• Hata, Itoh, Kugo
• Medicine
Physical review. D, Particles and fields
• 1987
Geometric String Field Theory: Deriving String Theory from First Principles
String field theory [1] gives us the greatest promise of a non-perturbative approach to string theory, but it is still plauged by a frustratingly large number of arbitrary conventions, folklore, and