## Algebras and differential equations |

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### Contents

Algebras | 1 |

Algebras and differential equations | 17 |

Some special invariant sets and subalgebras | 32 |

Copyright | |

7 other sections not shown

### Common terms and phrases

algebra V,p associative algebra associative bilinear form assume automorphism basis Chapter commutative complexification coordinates Corollary defined denote Der(V,p derivation dimension dimensional subalgebras direct sum eigenvalues elements Euler's equations existence ferential equation finite dimensional given gradient system hence homogeneous of degree homogeneous polynomial homomorphism idempotents and nilpotents identity implies invariant invertible isomorphism Jordan algebra Jordan pair Kasner's equation Lemma Lie algebra linear first integral linear map linearly independent m-ary algebra maximal ideals nondegenerate nontrivial Note obtain Obviously one-dimensional subalgebra polynomial differential equations polynomial map polynomial of degree polynomial semi-invariant power-associative prime divisors Proof Proposition qa(x rational first integrals Riccati equation semisimple shows skew-symmetric solution curves solution-preserving map solve stationary point subalgebra of Pol subspace symmetric Theorem 2.5 tion transitive subalgebra trivial uniquely determined vector space Volterra algebra Zariski-open zero