Group Theory, Algebra, and Number Theory: Colloquium in Memory of Hans Zassenhaus Held in Saarbrücken, Germany, June 4-5, 1993 (English and German Edition)

The 1987 landmark publications by G. Lakoff and M. Johnson made image schema one of the cornerstone concepts of the emerging experientialist paradigm of Cognitive Linguistics, a framework founded upon the rejection of the mind-body dichotomy and stressing the fundamentally embodied nature of meaning, imagination and reason - hence language. Conceived of as the pre-linguistic, dynamic and highly schematic gestalts arising directly from motor movement, object manipulation, and perceptual interaction, image schemas served to anchor abstract reasoning and imagination to sensori-motor patterns in the conceptual theory of metaphor. Being itself informed by preceding crosslinguistic work on semantic primitives in the linguistic representations of spatial relations (carried out by L. Talmy, R. Langacker, and others), the notion has inspired a large amount of subsequent research and debate on diverse issues ranging from the meaning, structure and acquisition of natural languages to the embodied mind itself. From Perception to Meaning is the first survey of current image-schema theory and offers a collection of original and innovative essays by leading scholars, many of whom have shaped the theory from the very beginning. The edition unites essays on major issues in recent research on image-schemas - from aspects of their definition and linguistic formalization, their psychological status and neural grounding to their role as semantic universals and primitives in language acquisition. The book will thus not only be welcomed by linguists of a cognitive orientation, but will prove relevant to philosophers, psychologists, and anthropologists interested in language, and indeed to anyone studying the embodied mind. Introductory address After-dinner speech On the solvability of the kernel of any orthogonal decomposition 1. Introduction 2. Lie algebras of types Bn,Cn, and Dn 3. Exceptional Lie algebras 4. Lie algebras of type An References The beginnings of modular Lie algebra theory 1. Introduction 2. Zassenhaus algebra 3. Lie algebras of Cartan type 4. Derivations 5. Sandwiches, filiations, ‘classicality’ criterion 6. Linear representations and Cartan prolongations 7. Lie algebras over fields of small characteristic 7.1. Characteristic p = 5 7.2. Characteristic p = 3 7.3. Characteristic p = 2 8. Miscellaneous References Computing invariants of algebraic number fields 1. Introduction 2. Galois groups 2.1. (B) Approximation of Γ from below 2.2. (A) Approximation of Γ from above and verification 3. Integral basis 3.1. Round 2-method 3.2. Round 4-method 4. Unit group and class group 4.1. Method I (assuming GRH) 4.2. Method II (unconditional) 5. Examples and applications References Kristallographische Gruppen 1. Einleitung 2. Die Periode bis 1950 aus heutiger Sicht 3. Die vierdimensionalen Raumgruppen 4. Spätere Entwicklungen 5. Beispiele von Bravaismannigfaltigkeiten Literatur Endliche Fastkörper und Zassenhausgruppen 1. Einleitung 2. Zur Kommutativität endlicher Divisionsringe 3. Gruppen mit Partition 4. Mehr über fixpunktfreie Operation 5. Gruppen mit pq-Bedingung 6. Ausnahmecharaktere und der SL2(5)-Satz von Zassenhaus 7. Das Isomorphieproblem 8. Die 2-dimensionalen linearen Gruppen und der SL2(5)-Satz von Dickson 9. Vollständige Fastkörper 10. Zassenhausgruppen Literatur On the arithmetic of commutative group rings 1. Introduction 2. Constructible units 3. Cyclic p-groups 4. Functors on cyclotomic algebras 4.1. Admissible functors 4.2. Cyclogenic functors 5. Local units and logarithms 5.1. Polarized bases 5.2. ogarithms and applications 6. Regular primes 6.1. Arithmetical background 6.2. Abelian p-groups 7. Irregular primes 7.1. A converse 7.2. Non-constructible units 8. Local units and global ideal classes 8.1. Normal bases for local units 8.2. Comparison with global units 8.3. Kernel groups 9. Cyclic groups of composite order 9.1. An exact sequence 9.2. Even order 9.3. Odd order References