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Page 5649 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
This interesting paper is a survey (not claiming to be comprehen- sive) of results on endomorphisms and automorphisms of relatively free associative and Lie algebras over a field K of characteristic 0  ...  (BG-AOS; Sofia) Endomorphisms and automorphisms of relatively free algebras. Recent developments in the theory of algebras with polynomial identities (Palermo, 1992). Rend. Circ. Mat.  ... 

Page 694 of American Journal of Mathematics Vol. 82, Issue 4 [page]

1960 American Journal of Mathematics  
Since any automorphism group of a Lie algebra induces an isomorphic automorphism group of any associated simply con- nected Lie group and every algebra has a simply connected, connected associated Lie  ...  Step one will consist in showing that there exists an infinite dimensional Lie algebra with certain properties.  ... 

Page 5416 of Mathematical Reviews Vol. , Issue 97I [page]

1997 Mathematical Reviews  
The main result of the paper under review is that the [A-automorphism group of the relatively free algebra F(V) of rank 2 cannot be generated by a finite subset of the [A-automorphism group of F(V) as  ...  In the case of the full automorphism group of free metabelian, nilpotent of class c Lie algebras of rank m, V. S. Drenski and C. K. Gupta [Canad. J.  ... 

Page 3082 of Mathematical Reviews Vol. , Issue 91F [page]

1991 Mathematical Reviews  
An automorphism of a relatively free group is called tame if it is induced by an automorphism of the absolutely free group of the same rank.  ...  of Lie type in the same characteristic to morphisms of algebraic groups.  ... 

A note on free presentations and residual nilpotence

B. Hartley
1984 Journal of Pure and Applied Algebra  
Thus it is essentiaily clear that a set of free generators of the relatively free group N will generate H freely as a relatively free Lie algebra.  ...  Now we recall some of the more elementary parts of the Andreev correspondence [2] between certain varieties of groups and Lie algebras.  ... 
doi:10.1016/0022-4049(84)90023-9 fatcat:iyi5rragezecfloympopkmojta

Page 1055 of Mathematical Reviews Vol. 21, Issue 10 [page]

1960 Mathematical Reviews  
The root system R of the linear algebraic group G is a subset of the character group X(T) of a maximal torus 7 of G, and X(T’) is a free abelian group of rank dim 7'.  ...  T and X are free abelian groups of rank dim 7’, and there exists a nondegenerate pairing of [ and X onto the additive group of integers.  ... 

Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in M_23 [article]

Sven Möller
2021 arXiv   pre-print
Scheithauer showed that there are exactly ten Borcherds-Kac-Moody algebras whose denominator identities are completely reflective automorphic products of singular weight on lattices of square-free level  ...  These belong to a larger class of Borcherds-Kac-Moody (super)algebras Borcherds obtained by twisting the denominator identity of the Fake Monster Lie algebra.  ...  Let ν be of square-free order m in M 23 . Then the real simple roots of g φν are the α ∈ ∆∩d∆ with α, α /2 = d for d | m and ρ, α = − α, α /2.  ... 
arXiv:1905.09629v2 fatcat:udxvi5ftcndmvpbfhuna34ob4q

Anosov Automorphisms of Nilpotent Lie Algebras [article]

Tracy L. Payne
2008 arXiv   pre-print
Each matrix A in GL_n(Z) naturally defines an automorphism f of the free r-step nilpotent Lie algebra on n generators.  ...  We study the relationship between the matrix A and the eigenvalues and rational invariant subspaces for f. We give applications to the study of Anosov automorphisms.  ...  We can also classify Anosov Lie algebras admitting automorphisms whose polynomials p 1 have certain specified Galois groups. Theorem 1.2.  ... 
arXiv:0809.3131v1 fatcat:leyve27mpngvncqfuw3zbuwkxq

Page 4045 of Mathematical Reviews Vol. , Issue 88h [page]

1988 Mathematical Reviews  
Math. 80 (1958), 458-538; MR 21 #1586] studied the relation between irreducible representations of a compact Lie group and certain algebraic homogeneous spaces of the group.  ...  Let G be a connected, semisimple algebraic group defined and split over Q; let o be an involutive automorphism over Q with fixed point group H and set XY = G/H.  ... 

Page 482 of Mathematical Reviews Vol. 33, Issue 3 [page]

1967 Mathematical Reviews  
representations of G, and the set of G-orbits, in the dual g* of the Lie algebra of G.  ...  , P is a closed characteristic subgroup of G, and G/P is the direct product of a vector group and a discrete torsion-free abelian group.  ... 

Representation stability for homotopy automorphisms [article]

Erik Lindell, Bashar Saleh
2022 arXiv   pre-print
Under certain conditions on the spaces and manifolds, we prove that the rational homotopy groups of these homotopy automorphisms form finitely generated FI-modules, and thus satisfy representation stability  ...  We consider in parallel pointed homotopy automorphisms of iterated wedge sums of topological spaces and boundary relative homotopy automorphisms of iterated connected sums of manifolds minus a disk.  ...  Let Aut ι L(H ⊕n , x, y) denote the group of ι-relative automorphisms of L(H ⊕n , x, y), and let ξ : Aut ι L(H ⊕n , x, y) → π 0 (aut ∂ Q (M Q n ) ) be the projection map that sends an ι-relative automorphism  ... 
arXiv:2105.11325v2 fatcat:dejqtkbqi5hf5itvubfyp6lrqy

The Pure Braid Groups and Their Relatives [chapter]

Alexander I. Suciu, He Wang
2017 Springer INdAM Series  
We also discuss several natural homomorphisms between these groups, and various ways to distinguish among the pure braid groups and their relatives.  ...  In this mostly survey paper, we investigate the resonance varieties, the lower central series ranks, and the Chen ranks, as well as the residual and formality properties of several families of braid-like  ...  Braid groups and their relatives Braid groups and pure braid groups Let Aut(F n ) be the group of (right) automorphisms of the free group F n on generators x 1 , . . . , x n .  ... 
doi:10.1007/978-3-319-58971-8_15 fatcat:jzxcbxnyvvbh5oebvqjzggag6a

Topological automorphism groups of compact quantum groups [article]

Alexandru Chirvasitu, Issan Patri
2017 arXiv   pre-print
For compact matrix quantum groups, which can be thought of as quantum analogues of compact Lie groups, we prove that the inner automorphism group is a compact Lie group and the outer automorphism group  ...  group and of the "inner" automorphism group coincide.  ...  Acknowledgements This work was initiated at the 7th ECM satellite conference "Compact Quantum Groups" at Greifswald, Germany and the authors are grateful to the organizers, Uwe Franz, Malte Gerhold, Adam  ... 
arXiv:1701.03885v1 fatcat:at23a2qk7nfelhavzqqy7bhty4

On Pro-p Groups Admitting a Fixed-Point-Free Automorphism

Pavel Shumyatsky
2000 Journal of Algebra  
ON LIE ALGEBRAS ADMITTING A FIXED-POINT-FREE AUTOMORPHISM An automorphism φ of a Lie algebra L is called fixed-point-free if C L φ = 0.  ...  We regard L as a Lie algebra over k ω and φ as an automorphism of L.  ... 
doi:10.1006/jabr.1999.8267 fatcat:dx65t3dqdnbxhhwscvzh4e3n2e

Page 764 of Mathematical Reviews Vol. 37, Issue 4 [page]

1969 Mathematical Reviews  
] (which may be, in particular, the category of associative, Lie, or commutative associative rings), and “ring” and “morphism” are meant relatively to @.  ...  Algebra 9 (1968), 212-219. Let A be a K-supplemented K algebra with augmentation ideal A, and let A= F/R present A as a free associative algebra (with unit) modulo an ideal.  ... 
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