2000/12/13 by Ron Fulp, Fulp, Ron, Tom Lada +3
Mathematics · Physics and Astronomy · #18G55 (Primary) 81T13 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #math-ph #math.MP #math.QA #msc:18G55 #msc:81T13
paper · pdf · doi:10.48550/arxiv.math/0012106
Now 24 pages, LaTeX, no figures Extensively revised in terms of the applications and on shell aspects. In particular, a new section 8 analyzes Ikeda's 2D example from our perspective. His bracket is revealed as a generalized Kirillov-Kostant bracket. Additional references
openalex publication_date 2000/12/13 · arxiv created 2001/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The physics of ``particles of spin ≤ 2'' leads to representations of a Lie algebra Ξ of gauge parameters on a vector space Φ of fields. Attempts to develop an analogous theory for spin >2 have failed; in fact, there are claims that such a theory is impossible (though we have been unable to determine the hypotheses for such a `no-go' theorem). This led BBvD [burgers:diss,BBvd:three,BBvD:probs] to generalize to `field dependent parameters' in a setting where some analysis in terms of smooth functions is possible. Having recognized the resulting structure as that of an sh-lie algebra (L_∞-algebra), we have now reproduced their structure entirely algebraically, hopefully shedding some light on what is going on.