LEADER 03566nam 2200661 450 001 9910717418803321 005 20240126164519.0 010 $a9783031274510$b(electronic bk.) 010 $z9783031274503 024 7 $a10.1007/978-3-031-27451-0 035 $a(MiAaPQ)EBC7241391 035 $a(Au-PeEL)EBL7241391 035 $a(OCoLC)1377816879 035 $a(DE-He213)978-3-031-27451-0 035 $a(PPN)269655476 035 $a(EXLCZ)9926523195700041 100 $a20230801d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHeat kernel on lie groups and maximally symmetric spaces /$fIvan G. Avramidi 205 $a1st ed. 2023. 210 1$aCham, Switzerland :$cSpringer Nature Switzerland AG,$d[2023] 210 4$d©2023 215 $a1 online resource (197 pages) 225 1 $aFrontiers in Mathematics,$x1660-8054 311 08$aPrint version: Avramidi, Ivan G. Heat Kernel on Lie Groups and Maximally Symmetric Spaces Cham : Springer International Publishing AG,c2023 9783031274503 320 $aIncludes bibliographical references and index. 327 $aPart I. Manifolds -- Chapter. 1. Introduction -- Chapter. 2. Geometry of Simple Groups -- Chapter. 3. Geometry of SU(2) -- Chapter. 4. Maximally Symmetric Spaces -- Chapter. 5. Three-dimensional Maximally Symmetric Spaces -- Part II: Heat Kernel -- Chapter. 6. Scalar Heat Kernel -- Chapter. 7. Spinor Heat Kernel -- Chapter. 8. Heat Kernel in Two Dimensions -- Chapter. 9. Heat Kernel on S3 and H3 -- Chapter. 10. Algebraic Method for the Heat Kernel -- Appendix A -- References -- Index. 330 $aThis monograph studies the heat kernel for the spin-tensor Laplacians on Lie groups and maximally symmetric spaces. It introduces many original ideas, methods, and tools developed by the author and provides a list of all known exact results in explicit form ? and derives them ? for the heat kernel on spheres and hyperbolic spaces. Part I considers the geometry of simple Lie groups and maximally symmetric spaces in detail, and Part II discusses the calculation of the heat kernel for scalar, spinor, and generic Laplacians on spheres and hyperbolic spaces in various dimensions. This text will be a valuable resource for researchers and graduate students working in various areas of mathematics ? such as global analysis, spectral geometry, stochastic processes, and financial mathematics ? as well in areas of mathematical and theoretical physics ? including quantum field theory, quantum gravity, string theory, and statistical physics. 410 0$aFrontiers in Mathematics,$x1660-8054 606 $aHeat equation 606 $aKernel functions 606 $aLie groups 606 $aSymmetric spaces 606 $aEquació de la calor$2thub 606 $aFuncions de Kernel$2thub 606 $aGrups de Lie$2thub 606 $aEspais simètrics$2thub 608 $aLlibres electrònics$2thub 615 0$aHeat equation. 615 0$aKernel functions. 615 0$aLie groups. 615 0$aSymmetric spaces. 615 7$aEquació de la calor 615 7$aFuncions de Kernel 615 7$aGrups de Lie 615 7$aEspais simètrics 676 $a515.353 700 $aAvramidi$b Ivan G.$f1957-$062541 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910717418803321 996 $aHeat Kernel on Lie Groups and Maximally Symmetric Spaces$93294466 997 $aUNINA