Contents

• Introduction
• Notations
  • A presentation of the full matrix algebra
  • light exponential function
  
  
• First properties of Weyl algebras
  • reduction to characteristic
  • Weyl algebras over fields of positive characteristics and their centers
  • Algebra endomorphisms and centers of Weyl algebras
  • A splitting algebra of
  • The quotient field of the Weyl algebra
  • definition of reduced trace and reduced norm
  • Algebra endomorphism and splitting of Weyl algebra
  • the geometric degree
  • uniqueness of an operator -th root for generators of
  • Algebra endomorphisms of Weyl algebras are determined by its restriction to the center
  
  
• Reduced trace and reduced norm
  • calculation of reduced trace
  • invariance of trace and inversion formula
  
  
• injectivity ()
  • comments on this section
  • injectivity()
  
  
• multidegree monoids and lattices
  • injectivity for almost all primes
  
  
• Bibliography