The tame and the wild automorphisms of an affine quadric threefold

The connexion between the conditions for five lines of S4(i) to lie upon a quadric threefold,and (ii) to be chords of a normal quartic curve,leads to an apparent contradiction. This difficulty is explained in the first paragraph below and, subsequently, two investigations are given of which the first uses, mainly, properties of space of three dimensions.

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Defining relations for tame automorphism groups of polynomial rings and wild automorphisms of free associative algebras

Doklady Mathematics ◽

10.1134/s1064562406020219 ◽

2006 ◽

Vol 73 (2) ◽

pp. 229-233

Author(s):

U. U. Umirbaev

Keyword(s):

Automorphism Groups ◽

Polynomial Rings ◽

Associative Algebras ◽

Defining Relations ◽

Tame Automorphism ◽

Wild Automorphisms

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Globally generated vector bundles of rank 2 on a smooth quadric threefold

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2013.05.005 ◽

2014 ◽

Vol 218 (2) ◽

pp. 197-207 ◽

Cited By ~ 7

Author(s):

E. Ballico ◽

S. Huh ◽

F. Malaspina

Keyword(s):

Vector Bundles ◽

Rank 2 ◽

Quadric Threefold

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On Tame and Wild Automorphisms of Algebras

Journal of Mathematical Sciences ◽

10.1007/s10958-015-2342-4 ◽

2015 ◽

Vol 206 (6) ◽

pp. 660-667

Author(s):

C. K. Gupta ◽

V. M. Levchuk ◽

Yu. Yu. Ushakov

Keyword(s):

Wild Automorphisms

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ON THE AUTOMORPHISM GROUP OF A FREE METABELIAN LIE ALGEBRA

International Journal of Algebra and Computation ◽

10.1142/s0218196708004408 ◽

2008 ◽

Vol 18 (02) ◽

pp. 209-226 ◽

Cited By ~ 5

Author(s):

VITALY ROMAN'KOV

Keyword(s):

Automorphism Group ◽

Normal Subgroup ◽

Lie Algebra ◽

Free Subgroup ◽

Finite Set ◽

Free Metabelian Lie Algebra ◽

Inner Automorphisms ◽

Infinite Set ◽

Wild Automorphisms

Let K be a field of any characteristic. We prove that a free metabelian Lie algebra M3 of rank 3 over K admits wild automorphisms. Moreover, the subgroup I Aut M3 of all automorphisms identical modulo the derived subalgebra [Formula: see text] cannot be generated by any finite set of IA-automorphisms together with the sets of all inner and all tame IA-automorphisms. In the case if K is finite the group Aut M3 cannot be generated by any finite set of automorphisms together with the sets of all tame, all inner automorphisms and all one-row automorphisms. We present an infinite set of wild IA-automorphisms of M3 which generates a free subgroup F∞ modulo normal subgroup generated by all tame, all inner and all one-row automorphisms of M3.

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