Cohomology of Conformal Algebras
نویسنده
چکیده
Introduction 2 1. Preliminaries on conformal algebras and modules 4 2. Basic definitions 9 3. Extensions and deformations 13 4. Homology 17 5. Exterior multiplication, contraction, and module structure 18 6. Cohomology of conformal algebras and their annihilation Lie algebras 19 6.1. Cohomology of the basic complex 19 6.2. Cohomology of the reduced complex 21 6.3. Cohomology of conformal algebras and formal distribution Lie algebras 22 7. Cohomology of the Virasoro conformal algebra 23 7.1. Cohomology of Vir with trivial coefficients 23 7.2. Cohomology of Vir with coefficients in M∆,α 25 8. Cohomology of current conformal algebras 27 8.1. Cohomology with trivial coefficients 27 8.2. Cohomology with coefficients in a current module 28 9. Hochschild, cyclic, and Lebniz cohomology 33 9.1. Hochschild cohomology 33 9.2. Cyclic cohomology 34 9.3. Leibniz cohomology 35 10. Generalization to conformal algebras in higher dimensions 36 11. Higher differentials 38 12. Relation to Lie algebras 40 13. Open problems 44 References 45
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