## Algebraic and Analytic Deformation Theory |

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### Contents

THE GRADED LIE ALGEBRA STRUCTURE 0F HAA | 6 |

ANALYTIC DEF0RMATI0N THE0RY | 17 |

ALGEBRAIC DEF0RMATI0N THE0RY I | 31 |

8 other sections not shown

### Common terms and phrases

0-cochain algebra automorphism algebra structure algebraic deformation analytic deformation cohomology associative algebra associative multiplication Chapter cochains cocycle coefficients of powers cohomologous to zero cohomology class cohomology theory commutative algebra compatible completes the proof complex analytic structures Consider corresponding defined definition deformation theory denote derivations differential operator discussion element enveloping associative algebra equivalence classes exact cohomology diagram existence exp(-tx extension of f f e HomP family of deformations finitely many obstructions formal power series germs of one-parameter Gerstenhaber given graded Lie algebra H A,M hence Hochschild cohomology HomP(T(A implies induced infinitesimal automorphism infinitesimal deformation injective inner automorphism integration isomorphism Jacobi identity kernel Krull topology Kuranishi Lemma Lie algebra structure linear manifolds Math n e Hom neighborhoods notation one-parameter family p+q=i p+q=r y Proposition pseudogroup right-hand side satisfying Section sequence sheaf of germs Spencer T-structure Theorem underlying vector space universal enveloping associative