论文标题
Weyl代数的热半群
Heat Semigroups on Weyl Algebra
论文作者
论文摘要
我们研究weyl代数的拉普拉斯人半群的代数。我们考虑一阶部分差分运算符$ \ nabla^\ pm_i $形成lie代数$ [\ nabla^\ pm_j，\ nabla^\ pm_k] = i \ Mathcal {r}^\ pm__ = i \ frac {1} {2}（\ Mathcal {r}^+_ {jk}+\ Mathcal {r}^ - _ {jk}）$，带有一些反对称矩阵$ \ MATHCAL {r} $δ_\ pm = g_ \ pm^{ij} \ nabla^\ pm_i \ nabla^\ pm_j $带有一些正矩阵$ g_ \ pm^{ij} $。 We show that the heat semigroups $\exp(tΔ_\pm)$ can be represented as a Gaussian average of the operators $\exp\left<ξ,\nabla^\pm\right>$ and use these representations to compute the product of the semigroups, $\exp(tΔ_+)\exp(sΔ_-)$ and the corresponding heat kernel.
We study the algebra of semigroups of Laplacians on the Weyl algebra. We consider first-order partial differential operators $\nabla^\pm_i$ forming the Lie algebra $[\nabla^\pm_j,\nabla^\pm_k]= i\mathcal{R}^\pm_{jk}$ and $[\nabla^+_j,\nabla^-_k] =i\frac{1}{2}(\mathcal{R}^+_{jk}+\mathcal{R}^-_{jk})$ with some anti-symmetric matrices $\mathcal{R}^\pm_{ij}$ and define the corresponding Laplacians $Δ_\pm=g_\pm^{ij}\nabla^\pm_i\nabla^\pm_j$ with some positive matrices $g_\pm^{ij}$. We show that the heat semigroups $\exp(tΔ_\pm)$ can be represented as a Gaussian average of the operators $\exp\left<ξ,\nabla^\pm\right>$ and use these representations to compute the product of the semigroups, $\exp(tΔ_+)\exp(sΔ_-)$ and the corresponding heat kernel.
