Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Home
  • Home
Hostname: page-component-559fc8cf4f-8sgpw Total loading time: 0.249 Render date: 2021-02-27T01:45:32.394Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }
EnglishFrançais
Nagoya Mathematical Journal Nagoya Mathematical Journal

Article contents

Tensor products of positive definite quadratic forms, V

Published online by Cambridge University Press:  22 January 2016

Yoshiyuki Kitaoka
Yoshiyuki Kitaoka
Affiliation:
Department of Mathematics, Faculty of Science, Nagoya University, Chikusa-ku, Nagoya, 464, Japan
Save pdf (1 mb)
Rights & Permissions[Opens in a new window]

Extract

Our aim is to prove

THEOREM. Let L be a positive lattice of E-type such that [L: L̃] < ∞ and L̃ is indecomposable.

  • (i) If L ≅ L 1 ⊗ L 2 for positive lattices L1, L2, then L1, L2 are of E-type and [L1: L̃1], [L2:L̃2] < ∞ and L̃1, L̃2 are indecomposable.
  • (ii) If L is indecomposable with respect to tensor product, then for each indecomposable positive lattice X we have
  • (1) L ⊗ X ≅ L ⊗ Y implies X ≅ Y for a positive lattice Y,
  • (2) If X= ⊗t L ⊗ X′ where X′ is not divided by L, then O(L ⊗ X) is generated by O(L), O(X′) and interchanges of L’s, and
  • (3) L ⊗ X is indecomposable.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 82 , June 1981 , pp. 99 - 111
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1981

References

[1] Kitaoka, Y., Scalar extension of quadratic lattices II, Nagoya Math. J., 67 (1977), 159–164.CrossRefGoogle Scholar
[2] Kitaoka, Y., Tensor products of positive definite quadratic forms, Göttingen Nachr. Nr., 4 (1977).Google Scholar
[3] Kitaoka, Y., Tensor products of positive definite quadratic forms II, J. reine angew. Math., 299/300 (1978), 161–170.Google Scholar
[4] Kitaoka, Y., Tensor products of positive definite quadratic forms IV, Nagoya Math. J., 73 (1979), 149–156.CrossRefGoogle Scholar
[5] O’Meara, O. T., Introduction to quadratic forms, Berlin-Heidelberg-New York, 1963.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 60 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 27th February 2021. This data will be updated every 24 hours.

Access
3 Cited by

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Tensor products of positive definite quadratic forms, V
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Tensor products of positive definite quadratic forms, V
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Tensor products of positive definite quadratic forms, V
Available formats
×
×

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *