Expository Notes

• Jordan–Chevalley Decomposition of Endomorphisms [PDF] ^{Last updated: Nov. 10, 2026}
  An expository note on the additive and multiplicative Jordan–Chevalley decompositions via $K[t]$-modules and the Chinese Remainder Theorem, together with properties of unipotent elements in zero and positive characteristics.

• Note on Braverman–Gaitsgory Theory [PDF] ^{Last updated: Nov. 10, 2026}
  An exposition of the Poincaré–Birkhoff–Witt (PBW) deformation theorem for Koszul algebras via graded deformations and Hochschild cohomology.