Second cohomology of $\mathfrak{aff}(1)$ acting on $n$-ary differential operators
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We compute the second cohomology of the affine Lie algebra $\mathfrak{aff}(1)$ on the dimensional real space with coefficients in the space $\mathcal{D}^n_{\underline{\lambda},\mu}$ of $n$-ary linear differential operators acting on weighted densities where $\underline{\lambda}=(\lambda_1,\ldots,\lambda_n)$. We explicitly give $2$-cocycles spanning these cohomology.
Abstract
We compute the second cohomology of the affine Lie algebra $\mathfrak{aff}(1)$ on the dimensional real space with coefficients in the space $\mathcal{D}^n_{\underline{\lambda},\mu}$ of $n$-ary linear differential operators acting on weighted densities where $\underline{\lambda}=(\lambda_1,\ldots,\lambda_n)$. We explicitly give $2$-cocycles spanning these cohomology.
참고문헌 (14)
- I. Basdouri, "The linear aff(n|1)-invariant differential operators on weighted densities on the superspace R1|n and aff(n|1)-relative cohomology", Int. J. Geom. Methods Mod. Phys, 10(4), pp.9~ (2013)
- G. G. A. Bauerle, "Lie algebras. Part 1" (1990), North-Holland Publishing Co.
- G. G. A. Bauerle, "Finite and infinite dimensional Lie algebras and their application in physics" (1997), North-Holland
- G. Dito, "Deformation quantization and Nambu mechanics", Comm. Math. Phys, 183(1), pp.1~22 (1997)
- G. Dito, "Deformation quantization: genesis, developments and meta-morphoses", pp.9~54 (2002), Walter De Gruyter
- J.-P. Francoise, "Current Algebra" (2006), Science Direct
- D. B. Fuks, "Contemporary Soviet Mathematics" (1986), Consultants Bureau
- P. Goddard, "VIIIth international congress on mathematical physics", pp.390~401 (1987), World Sci. Publishing
- V. G. Kac, "Infinite-dimensional Lie algebras" (1990), Cambridge Uni. Press
- A. A. Kirillov, "Elementy teorii predstavlenii" (1972), Nauka
- A. A. Kirillov, "Current problems in mathematics, Itogi Nauki i Tekhniki", pp.141~178 (1985), Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform.
- A. W. Knapp, "Lie groups beyond an introduction" (2002), Birkhauser Boston, Inc.
- B. Kostant, "Lectures in modern analysis and applications, III", pp.87~208 (1970), Springer
- D. Sternheimer, "Deformation theory and symplectic geome-try" (1997), Kluwer Academic Publishers Group