论文标题
Hirzebruch-Riemann-Roch和Lefschetz类型的有限尺寸代数的公式
Hirzebruch-Riemann-Roch and Lefschetz type formulas for finite dimensional algebras
论文作者
论文摘要
明确给出了有限维度的全球维度代数的Hirzebuch-Riemann-Roch（HRR）和Lefschetz类型公式。它们具有共同的，同源性，Hochschild共同体和Hochschild同源性四个版本，以及模块，双模块，模块复合物和Bimodule复合物四个级别。为此，引入了双模模（复合物）的尺寸矩阵和双模块（复杂）内态的痕量矩阵。结果表明，在这种情况下，Cartan矩阵，Dimension Vector和Trace Vector可以具体表达Shklyarov配对，Chern角色和Hattori-Stallings Trace。此外，比较了有限的全局尺寸和DG代数的有限维数代数的HRR和LEFSCHETZ型公式。
The Hirzebuch-Riemann-Roch (HRR) and Lefschetz type formulas for finite dimensional elementary algebras of finite global dimension are explicitly given. They have cohomological, homological, Hochschild cohomological and Hochschild homological four versions, and module, bimodule, module complex and bimodule complex four levels. For this, the dimension matrix of a bimodule (complex) and the trace matrix of a bimodule (complex) endomorphism are introduced. It is shown that Shklyarov pairing, Chern character and Hattori-Stallings trace can be concretely expressed by Cartan matrix, dimension vector and trace vector in this situation. Furthermore, the HRR and Lefschetz type formulas for finite dimensional elementary algebras of finite global dimension and dg algebras are compared.
