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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.
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참고문헌 (14)
참고문헌 신청
I. Basdouri / 2013 / 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):9
G. G. A. Bauerle / 1990 / Lie algebras. Part 1 / North-Holland Publishing Co.
G. G. A. Bauerle / 1997 / Finite and infinite dimensional Lie algebras and their application in physics / North-Holland
G. Dito / 1997 / Deformation quantization and Nambu mechanics / Comm. Math. Phys 183(1):1~22
G. Dito / 2002 / Deformation quantization: genesis, developments and meta-morphoses / Walter De Gruyter :9~54
G. G. A. Bauerle / 1990 / Lie algebras. Part 1 / North-Holland Publishing Co.
G. G. A. Bauerle / 1997 / Finite and infinite dimensional Lie algebras and their application in physics / North-Holland
G. Dito / 1997 / Deformation quantization and Nambu mechanics / Comm. Math. Phys 183(1):1~22
G. Dito / 2002 / Deformation quantization: genesis, developments and meta-morphoses / Walter De Gruyter :9~54
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